Symplectic automorphisms of prime order on K3 surfaces

被引：36

作者：

Garbagnati, Alice ^{[2
]}

Sarti, Alessandra ^{[1
]}

机构：

[1] Johannes Gutenberg Univ Mainz, Inst Math, D-55099 Mainz, Germany

[2] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

JOURNAL OF ALGEBRA | 2007年 / 318卷 / 01期

关键词：

K3; surfaces; automorphisms; moduli;

D O I：

10.1016/j.jalgebra.2007.04.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study algebraic K3 surfaces (defined over the complex number field) with a symplectic automorphism of prime order. In particular we consider the action of the automorphism on the second cohomology with integer coefficients (by a result of Nikulin this action is independent on the choice of the K3 surface). With the help of elliptic fibrations we determine the invariant sublattice and its perpendicular complement, and show that the latter coincides with the Coxeter-Todd lattice in the case of automorphism of order three. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：323 / 350

页数：28

共 24 条

[1]

[Anonymous], 1994, ADV LECT MATH

[2]

BARTH W, 1984, ERGEB MATH GRENZGEB

[3] Modular lattices over cyclotomic fields [J].