The Kodaira dimension of the moduli of K3 surfaces

Abstract The global Torelli theorem for projective K3 surfaces was first proved by Piatetskii-Shapiro and Shafarevich 35 years ago, opening the way to treating moduli problems for K3 surfaces. The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective variety of dimension 19. For g...
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Autor*in:	Gritsenko, V.A. [verfasserIn] Hulek, K. Sankaran, G.K.

Format:	Artikel
Sprache:	Englisch

Erschienen:	2007

Schlagwörter:	Modulus Space Modular Form Toric Variety Orthogonal Complement Cusp Form

Systematik:	SA 5940 SA 5940

Anmerkung:	© Springer-Verlag 2007

Übergeordnetes Werk:	Enthalten in: Inventiones mathematicae - Springer-Verlag, 1966, 169(2007), 3 vom: 12. Mai, Seite 519-567
Übergeordnetes Werk:	volume:169 ; year:2007 ; number:3 ; day:12 ; month:05 ; pages:519-567

Links:	Volltext

DOI / URN:	10.1007/s00222-007-0054-1

Katalog-ID:	OLC2050921322

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spelling	10.1007/s00222-007-0054-1 doi (DE-627)OLC2050921322 (DE-He213)s00222-007-0054-1-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn SA 5940 VZ rvk SA 5940 VZ rvk Gritsenko, V.A. verfasserin aut The Kodaira dimension of the moduli of K3 surfaces 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2007 Abstract The global Torelli theorem for projective K3 surfaces was first proved by Piatetskii-Shapiro and Shafarevich 35 years ago, opening the way to treating moduli problems for K3 surfaces. The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective variety of dimension 19. For general d very little has been known hitherto about the Kodaira dimension of these varieties. In this paper we present an almost complete solution to this problem. Our main result says that this moduli space is of general type for d>61 and for d=46, 50, 54, 57, 58, 60. Modulus Space Modular Form Toric Variety Orthogonal Complement Cusp Form Hulek, K. aut Sankaran, G.K. aut Enthalten in Inventiones mathematicae Springer-Verlag, 1966 169(2007), 3 vom: 12. Mai, Seite 519-567 (DE-627)129077453 (DE-600)2921-X (DE-576)014409992 0020-9910 nnns volume:169 year:2007 number:3 day:12 month:05 pages:519-567 https://doi.org/10.1007/s00222-007-0054-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 5940 SA 5940 AR 169 2007 3 12 05 519-567
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allfieldsSound	10.1007/s00222-007-0054-1 doi (DE-627)OLC2050921322 (DE-He213)s00222-007-0054-1-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn SA 5940 VZ rvk SA 5940 VZ rvk Gritsenko, V.A. verfasserin aut The Kodaira dimension of the moduli of K3 surfaces 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2007 Abstract The global Torelli theorem for projective K3 surfaces was first proved by Piatetskii-Shapiro and Shafarevich 35 years ago, opening the way to treating moduli problems for K3 surfaces. The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective variety of dimension 19. For general d very little has been known hitherto about the Kodaira dimension of these varieties. In this paper we present an almost complete solution to this problem. Our main result says that this moduli space is of general type for d>61 and for d=46, 50, 54, 57, 58, 60. Modulus Space Modular Form Toric Variety Orthogonal Complement Cusp Form Hulek, K. aut Sankaran, G.K. aut Enthalten in Inventiones mathematicae Springer-Verlag, 1966 169(2007), 3 vom: 12. Mai, Seite 519-567 (DE-627)129077453 (DE-600)2921-X (DE-576)014409992 0020-9910 nnns volume:169 year:2007 number:3 day:12 month:05 pages:519-567 https://doi.org/10.1007/s00222-007-0054-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2021 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 5940 SA 5940 AR 169 2007 3 12 05 519-567
language	English
source	Enthalten in Inventiones mathematicae 169(2007), 3 vom: 12. Mai, Seite 519-567 volume:169 year:2007 number:3 day:12 month:05 pages:519-567
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topic_facet	Modulus Space Modular Form Toric Variety Orthogonal Complement Cusp Form
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author	Gritsenko, V.A.
spellingShingle	Gritsenko, V.A. ddc 510 ssgn 17,1 rvk SA 5940 misc Modulus Space misc Modular Form misc Toric Variety misc Orthogonal Complement misc Cusp Form The Kodaira dimension of the moduli of K3 surfaces
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title	The Kodaira dimension of the moduli of K3 surfaces
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title_full	The Kodaira dimension of the moduli of K3 surfaces
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title_sort	the kodaira dimension of the moduli of k3 surfaces
title_auth	The Kodaira dimension of the moduli of K3 surfaces
abstract	Abstract The global Torelli theorem for projective K3 surfaces was first proved by Piatetskii-Shapiro and Shafarevich 35 years ago, opening the way to treating moduli problems for K3 surfaces. The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective variety of dimension 19. For general d very little has been known hitherto about the Kodaira dimension of these varieties. In this paper we present an almost complete solution to this problem. Our main result says that this moduli space is of general type for d>61 and for d=46, 50, 54, 57, 58, 60. © Springer-Verlag 2007
abstractGer	Abstract The global Torelli theorem for projective K3 surfaces was first proved by Piatetskii-Shapiro and Shafarevich 35 years ago, opening the way to treating moduli problems for K3 surfaces. The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective variety of dimension 19. For general d very little has been known hitherto about the Kodaira dimension of these varieties. In this paper we present an almost complete solution to this problem. Our main result says that this moduli space is of general type for d>61 and for d=46, 50, 54, 57, 58, 60. © Springer-Verlag 2007
abstract_unstemmed	Abstract The global Torelli theorem for projective K3 surfaces was first proved by Piatetskii-Shapiro and Shafarevich 35 years ago, opening the way to treating moduli problems for K3 surfaces. The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective variety of dimension 19. For general d very little has been known hitherto about the Kodaira dimension of these varieties. In this paper we present an almost complete solution to this problem. Our main result says that this moduli space is of general type for d>61 and for d=46, 50, 54, 57, 58, 60. © Springer-Verlag 2007
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title_short	The Kodaira dimension of the moduli of K3 surfaces
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