Moduli spaces of irreducible symplectic manifolds

被引：58
作者：
Gritsenko, V. [1 ]
Hulek, K. [2 ]
Sankaran, G. K. [3 ]
机构：
[1] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve Dascq, France
[2] Leibniz Univ Hannover, Inst Algebra Geometrie, D-30060 Hannover, Germany
[3] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England
来源：
COMPOSITIO MATHEMATICA | 2010年 / 146卷 / 02期
关键词：
irreducible symplectic manifold; moduli; orthogonal groups; Siegel formula for quadratic forms; COMPACT HYPERKAHLER MANIFOLDS; K3; SURFACES; KODAIRA DIMENSION; COUNTER-EXAMPLE; QUADRATIC-FORMS; TORELLI THEOREM; THREEFOLDS; INTEGERS; 4-FOLDS; SHEAVES;
D O I：
10.1112/S0010437X0900445X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the moduli spaces of polarised irreducible symplectic manifolds. By a comparison with locally symmetric varieties of orthogonal type of dimension 20, we show that the moduli space of polarised deformation K3([2]) manifolds with polarisation of degree 2d and split type is of general type if d >= 12.
引用
收藏
页码：404 / 434
页数：31
相关论文
共 51 条
[1]  
[Anonymous], 1992, J. Algebraic Geom.
[2]  
[Anonymous], 1985, Algebraic geometry, Sendai
[3]  
[Anonymous], 1988, GRUNDLEHREN MATH WIS
[4]  
[Anonymous], 1987, SMOOTHNESS UNIVERSAL
[5]  
BEAUVILLE A, 1983, J DIFFER GEOM, V18, P755
[6]  
BOGOMOLOV FA, 1978, DOKL AKAD NAUK SSSR+, V243, P1101
[7]  
Borcherds RE, 1998, J ALGEBRAIC GEOM, V7, P183
[8]   AUTOMORPHIC-FORMS ON O-S+2,O-2(R) AND INFINITE PRODUCTS [J].
BORCHERDS, RE .
INVENTIONES MATHEMATICAE, 1995, 120 (01) :161-213
[9]  
Borel Bor72 Armand, 1972, Jour. Diff. Geom., V6, P543
[10]  
BOURBAKI N, 1968, GROUPES ALGEBRES LIE, pCH4
123456