Behavior of the Fiber and the Base Points of Parametrizations Under Projections
Abstract Given a rational parametrization %${{\mathcal{P}(\overline {t}), {\overline {t}}=(t_1, \ldots, t_r)}}%$ , of an r-dimensional unirational variety, we analyze the behavior of the variety of the base points of %${\mathcal{P}(\overline {t})}%$ in connection to its generic fibre, when successiv...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Pérez-Díaz, Sonia [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Basel 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Mathematics in computer science - Cham (ZG) : Springer International Publishing AG, 2007, 7(2013), 2 vom: 24. Jan., Seite 167-184 |
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| Übergeordnetes Werk: |
volume:7 ; year:2013 ; number:2 ; day:24 ; month:01 ; pages:167-184 |
| Links: |
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| DOI / URN: |
10.1007/s11786-013-0139-8 |
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| Katalog-ID: |
SPR022424695 |
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| 100 | 1 | |a Pérez-Díaz, Sonia |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Behavior of the Fiber and the Base Points of Parametrizations Under Projections |
| 264 | 1 | |c 2013 | |
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| 500 | |a © Springer Basel 2013 | ||
| 520 | |a Abstract Given a rational parametrization %${{\mathcal{P}(\overline {t}), {\overline {t}}=(t_1, \ldots, t_r)}}%$ , of an r-dimensional unirational variety, we analyze the behavior of the variety of the base points of %${\mathcal{P}(\overline {t})}%$ in connection to its generic fibre, when successively eliminating the parameters ti. For this purpose. we introduce a sequence of generalized resultants whose primitive and content parts contain the different components of the projected variety of the base points and the fibre. In addition, when the dimension of the base points is strictly smaller than 1 (as in the well known cases of curves and surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the corresponding Gröbner basis of the ideal associated to the fibre; assuming that the ideal is in t1-general position and radical. | ||
| 650 | 4 | |a Rational parametrization |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Unirational variety |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Degree of a rational map |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Fiber of a rational map |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Base points |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Generalized resultants |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Sendra, J. Rafael |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Mathematics in computer science |d Cham (ZG) : Springer International Publishing AG, 2007 |g 7(2013), 2 vom: 24. Jan., Seite 167-184 |w (DE-627)548639310 |w (DE-600)2394773-1 |x 1661-8289 |7 nnns |
| 773 | 1 | 8 | |g volume:7 |g year:2013 |g number:2 |g day:24 |g month:01 |g pages:167-184 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s11786-013-0139-8 |z lizenzpflichtig |3 Volltext |
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2013 |
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10.1007/s11786-013-0139-8 doi (DE-627)SPR022424695 (SPR)s11786-013-0139-8-e DE-627 ger DE-627 rakwb eng Pérez-Díaz, Sonia verfasserin aut Behavior of the Fiber and the Base Points of Parametrizations Under Projections 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2013 Abstract Given a rational parametrization %${{\mathcal{P}(\overline {t}), {\overline {t}}=(t_1, \ldots, t_r)}}%$ , of an r-dimensional unirational variety, we analyze the behavior of the variety of the base points of %${\mathcal{P}(\overline {t})}%$ in connection to its generic fibre, when successively eliminating the parameters ti. For this purpose. we introduce a sequence of generalized resultants whose primitive and content parts contain the different components of the projected variety of the base points and the fibre. In addition, when the dimension of the base points is strictly smaller than 1 (as in the well known cases of curves and surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the corresponding Gröbner basis of the ideal associated to the fibre; assuming that the ideal is in t1-general position and radical. Rational parametrization (dpeaa)DE-He213 Unirational variety (dpeaa)DE-He213 Degree of a rational map (dpeaa)DE-He213 Fiber of a rational map (dpeaa)DE-He213 Base points (dpeaa)DE-He213 Generalized resultants (dpeaa)DE-He213 Sendra, J. Rafael aut Enthalten in Mathematics in computer science Cham (ZG) : Springer International Publishing AG, 2007 7(2013), 2 vom: 24. Jan., Seite 167-184 (DE-627)548639310 (DE-600)2394773-1 1661-8289 nnns volume:7 year:2013 number:2 day:24 month:01 pages:167-184 https://dx.doi.org/10.1007/s11786-013-0139-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 7 2013 2 24 01 167-184 |
| spelling |
10.1007/s11786-013-0139-8 doi (DE-627)SPR022424695 (SPR)s11786-013-0139-8-e DE-627 ger DE-627 rakwb eng Pérez-Díaz, Sonia verfasserin aut Behavior of the Fiber and the Base Points of Parametrizations Under Projections 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2013 Abstract Given a rational parametrization %${{\mathcal{P}(\overline {t}), {\overline {t}}=(t_1, \ldots, t_r)}}%$ , of an r-dimensional unirational variety, we analyze the behavior of the variety of the base points of %${\mathcal{P}(\overline {t})}%$ in connection to its generic fibre, when successively eliminating the parameters ti. For this purpose. we introduce a sequence of generalized resultants whose primitive and content parts contain the different components of the projected variety of the base points and the fibre. In addition, when the dimension of the base points is strictly smaller than 1 (as in the well known cases of curves and surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the corresponding Gröbner basis of the ideal associated to the fibre; assuming that the ideal is in t1-general position and radical. Rational parametrization (dpeaa)DE-He213 Unirational variety (dpeaa)DE-He213 Degree of a rational map (dpeaa)DE-He213 Fiber of a rational map (dpeaa)DE-He213 Base points (dpeaa)DE-He213 Generalized resultants (dpeaa)DE-He213 Sendra, J. Rafael aut Enthalten in Mathematics in computer science Cham (ZG) : Springer International Publishing AG, 2007 7(2013), 2 vom: 24. Jan., Seite 167-184 (DE-627)548639310 (DE-600)2394773-1 1661-8289 nnns volume:7 year:2013 number:2 day:24 month:01 pages:167-184 https://dx.doi.org/10.1007/s11786-013-0139-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 7 2013 2 24 01 167-184 |
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10.1007/s11786-013-0139-8 doi (DE-627)SPR022424695 (SPR)s11786-013-0139-8-e DE-627 ger DE-627 rakwb eng Pérez-Díaz, Sonia verfasserin aut Behavior of the Fiber and the Base Points of Parametrizations Under Projections 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2013 Abstract Given a rational parametrization %${{\mathcal{P}(\overline {t}), {\overline {t}}=(t_1, \ldots, t_r)}}%$ , of an r-dimensional unirational variety, we analyze the behavior of the variety of the base points of %${\mathcal{P}(\overline {t})}%$ in connection to its generic fibre, when successively eliminating the parameters ti. For this purpose. we introduce a sequence of generalized resultants whose primitive and content parts contain the different components of the projected variety of the base points and the fibre. In addition, when the dimension of the base points is strictly smaller than 1 (as in the well known cases of curves and surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the corresponding Gröbner basis of the ideal associated to the fibre; assuming that the ideal is in t1-general position and radical. Rational parametrization (dpeaa)DE-He213 Unirational variety (dpeaa)DE-He213 Degree of a rational map (dpeaa)DE-He213 Fiber of a rational map (dpeaa)DE-He213 Base points (dpeaa)DE-He213 Generalized resultants (dpeaa)DE-He213 Sendra, J. Rafael aut Enthalten in Mathematics in computer science Cham (ZG) : Springer International Publishing AG, 2007 7(2013), 2 vom: 24. Jan., Seite 167-184 (DE-627)548639310 (DE-600)2394773-1 1661-8289 nnns volume:7 year:2013 number:2 day:24 month:01 pages:167-184 https://dx.doi.org/10.1007/s11786-013-0139-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 7 2013 2 24 01 167-184 |
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10.1007/s11786-013-0139-8 doi (DE-627)SPR022424695 (SPR)s11786-013-0139-8-e DE-627 ger DE-627 rakwb eng Pérez-Díaz, Sonia verfasserin aut Behavior of the Fiber and the Base Points of Parametrizations Under Projections 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2013 Abstract Given a rational parametrization %${{\mathcal{P}(\overline {t}), {\overline {t}}=(t_1, \ldots, t_r)}}%$ , of an r-dimensional unirational variety, we analyze the behavior of the variety of the base points of %${\mathcal{P}(\overline {t})}%$ in connection to its generic fibre, when successively eliminating the parameters ti. For this purpose. we introduce a sequence of generalized resultants whose primitive and content parts contain the different components of the projected variety of the base points and the fibre. In addition, when the dimension of the base points is strictly smaller than 1 (as in the well known cases of curves and surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the corresponding Gröbner basis of the ideal associated to the fibre; assuming that the ideal is in t1-general position and radical. Rational parametrization (dpeaa)DE-He213 Unirational variety (dpeaa)DE-He213 Degree of a rational map (dpeaa)DE-He213 Fiber of a rational map (dpeaa)DE-He213 Base points (dpeaa)DE-He213 Generalized resultants (dpeaa)DE-He213 Sendra, J. Rafael aut Enthalten in Mathematics in computer science Cham (ZG) : Springer International Publishing AG, 2007 7(2013), 2 vom: 24. Jan., Seite 167-184 (DE-627)548639310 (DE-600)2394773-1 1661-8289 nnns volume:7 year:2013 number:2 day:24 month:01 pages:167-184 https://dx.doi.org/10.1007/s11786-013-0139-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 7 2013 2 24 01 167-184 |
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10.1007/s11786-013-0139-8 doi (DE-627)SPR022424695 (SPR)s11786-013-0139-8-e DE-627 ger DE-627 rakwb eng Pérez-Díaz, Sonia verfasserin aut Behavior of the Fiber and the Base Points of Parametrizations Under Projections 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2013 Abstract Given a rational parametrization %${{\mathcal{P}(\overline {t}), {\overline {t}}=(t_1, \ldots, t_r)}}%$ , of an r-dimensional unirational variety, we analyze the behavior of the variety of the base points of %${\mathcal{P}(\overline {t})}%$ in connection to its generic fibre, when successively eliminating the parameters ti. For this purpose. we introduce a sequence of generalized resultants whose primitive and content parts contain the different components of the projected variety of the base points and the fibre. In addition, when the dimension of the base points is strictly smaller than 1 (as in the well known cases of curves and surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the corresponding Gröbner basis of the ideal associated to the fibre; assuming that the ideal is in t1-general position and radical. Rational parametrization (dpeaa)DE-He213 Unirational variety (dpeaa)DE-He213 Degree of a rational map (dpeaa)DE-He213 Fiber of a rational map (dpeaa)DE-He213 Base points (dpeaa)DE-He213 Generalized resultants (dpeaa)DE-He213 Sendra, J. Rafael aut Enthalten in Mathematics in computer science Cham (ZG) : Springer International Publishing AG, 2007 7(2013), 2 vom: 24. Jan., Seite 167-184 (DE-627)548639310 (DE-600)2394773-1 1661-8289 nnns volume:7 year:2013 number:2 day:24 month:01 pages:167-184 https://dx.doi.org/10.1007/s11786-013-0139-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 7 2013 2 24 01 167-184 |
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Enthalten in Mathematics in computer science 7(2013), 2 vom: 24. Jan., Seite 167-184 volume:7 year:2013 number:2 day:24 month:01 pages:167-184 |
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Mathematics in computer science |
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Pérez-Díaz, Sonia @@aut@@ Sendra, J. Rafael @@aut@@ |
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Pérez-Díaz, Sonia |
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Pérez-Díaz, Sonia misc Rational parametrization misc Unirational variety misc Degree of a rational map misc Fiber of a rational map misc Base points misc Generalized resultants Behavior of the Fiber and the Base Points of Parametrizations Under Projections |
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Behavior of the Fiber and the Base Points of Parametrizations Under Projections Rational parametrization (dpeaa)DE-He213 Unirational variety (dpeaa)DE-He213 Degree of a rational map (dpeaa)DE-He213 Fiber of a rational map (dpeaa)DE-He213 Base points (dpeaa)DE-He213 Generalized resultants (dpeaa)DE-He213 |
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misc Rational parametrization misc Unirational variety misc Degree of a rational map misc Fiber of a rational map misc Base points misc Generalized resultants |
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misc Rational parametrization misc Unirational variety misc Degree of a rational map misc Fiber of a rational map misc Base points misc Generalized resultants |
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Behavior of the Fiber and the Base Points of Parametrizations Under Projections |
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Behavior of the Fiber and the Base Points of Parametrizations Under Projections |
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behavior of the fiber and the base points of parametrizations under projections |
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Behavior of the Fiber and the Base Points of Parametrizations Under Projections |
| abstract |
Abstract Given a rational parametrization %${{\mathcal{P}(\overline {t}), {\overline {t}}=(t_1, \ldots, t_r)}}%$ , of an r-dimensional unirational variety, we analyze the behavior of the variety of the base points of %${\mathcal{P}(\overline {t})}%$ in connection to its generic fibre, when successively eliminating the parameters ti. For this purpose. we introduce a sequence of generalized resultants whose primitive and content parts contain the different components of the projected variety of the base points and the fibre. In addition, when the dimension of the base points is strictly smaller than 1 (as in the well known cases of curves and surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the corresponding Gröbner basis of the ideal associated to the fibre; assuming that the ideal is in t1-general position and radical. © Springer Basel 2013 |
| abstractGer |
Abstract Given a rational parametrization %${{\mathcal{P}(\overline {t}), {\overline {t}}=(t_1, \ldots, t_r)}}%$ , of an r-dimensional unirational variety, we analyze the behavior of the variety of the base points of %${\mathcal{P}(\overline {t})}%$ in connection to its generic fibre, when successively eliminating the parameters ti. For this purpose. we introduce a sequence of generalized resultants whose primitive and content parts contain the different components of the projected variety of the base points and the fibre. In addition, when the dimension of the base points is strictly smaller than 1 (as in the well known cases of curves and surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the corresponding Gröbner basis of the ideal associated to the fibre; assuming that the ideal is in t1-general position and radical. © Springer Basel 2013 |
| abstract_unstemmed |
Abstract Given a rational parametrization %${{\mathcal{P}(\overline {t}), {\overline {t}}=(t_1, \ldots, t_r)}}%$ , of an r-dimensional unirational variety, we analyze the behavior of the variety of the base points of %${\mathcal{P}(\overline {t})}%$ in connection to its generic fibre, when successively eliminating the parameters ti. For this purpose. we introduce a sequence of generalized resultants whose primitive and content parts contain the different components of the projected variety of the base points and the fibre. In addition, when the dimension of the base points is strictly smaller than 1 (as in the well known cases of curves and surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the corresponding Gröbner basis of the ideal associated to the fibre; assuming that the ideal is in t1-general position and radical. © Springer Basel 2013 |
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Behavior of the Fiber and the Base Points of Parametrizations Under Projections |
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Sendra, J. Rafael |
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