Irreducible symplectic 4-folds numerically equivalent to (K3)[2]

被引:23
作者
O'Grady, Kieran G. [1 ]
机构
[1] Univ Roma La Sapienza, Dipartimento Matemat Guido Castelnuovo, I-00185 Rome, Italy
关键词
holomorphic symplectic 4-fold; linear system;
D O I
10.1142/S0219199708002909
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
First steps toward a classification of irreducible symplectic 4-folds whose integral 2-cohomology with 4-tuple cup product is isomorphic to that of (K3)([2]). We prove that any such 4-fold deforms to an irreducible symplectic 4-fold of Type A or Type B. A 4-fold of Type A is a double cover of a (singular) sextic hypersurface and a 4-fold of Type B is birational to a hypersurface of degree at most 12. We conjecture that Type B 4-folds do not exist.
引用
收藏
页码:553 / 608
页数:56
相关论文
共 25 条
[1]  
BEAUVILLE A, 1983, J DIFFER GEOM, V18, P755
[2]  
BEAUVILLE A, 1985, CR ACAD SCI I-MATH, V301, P703
[3]  
BEAUVILLE A, 1985, ASTERISQUE
[4]  
Casnati G, 1997, J DIFFER GEOM, V47, P237
[5]   Weakly defective varieties [J].
Chiantini, L ;
Ciliberto, C .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 354 (01) :151-178
[6]  
Debarre O, 1998, MATH ANN, V312, P549, DOI 10.1007/s002080050235
[7]  
DELIGNE P, 1974, PUBLICATIONS MATH IH, V44, P5, DOI 10.1007/BF02685881
[8]   Lagrangian subbundles and codimension 3 subcanonical subschemes [J].
Eisenbud, D ;
Popescu, S ;
Walter, C .
DUKE MATHEMATICAL JOURNAL, 2001, 107 (03) :427-467
[9]  
Fujiki A., 1987, ADV STUDIES PURE MAT, V10, P105
[10]  
Fulton W., 1984, INTERSECTION THEORY