Automorphisms of Enriques surfaces
Automorphisms of Enriques surfaces
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DOI：
10.1007/bf01388435
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发表时间：
1983-10
影响因子：
3.1
通讯作者：
W. Barth;C. Peters
中科院分区：
文献类型：
--
作者：
W. Barth;C. Peters
本文的目的是计算一般Enriques曲面Y的（双全纯）自同构群Aut（Y）。基本工具是投影K3-曲面的整体Torelli定理，它由Piatetski-Shapiro和Shafarevich [11]给出，并由Burns和Rapaport [2]改进。其基本结果是，与曲线的情况相反，Aut（Y）对于一般Y是大的，对于特殊Y是小的。回想一下，Enriques曲面Y是一个（射影）复曲面，其泛二重覆盖是K3-曲面。我们知道H2（Y，Z）= 7Z，2~ 2，并且杯积为HE（y，71）/挠率=~ 1~提供了签名为（1，9）的格M的结构。
The aim of this note is to compute the group Aut (Y) of (biholomorphic) automorphisms for the general Enriques surface Y. The basic tool is the global Torelli theorem for projective K3-surfaces as it was given by Piatetski-Shapiro and Shafarevich [11] and refined by Burns and Rapaport [2]. The essential result is that-in contrast to the case of curves-Aut (Y) is big for general Y and small for special Y.In this paper we consider the complex case only. Recall that an Enriques surface Y is a (projective) complex surface with universal double cover a K3-surface. One knows that H2 (Y, Z)= 7Z, 2~ 2 and that the cup-product provides HE (y, 71)/torsion=~ 1~ with the structure of a lattice M of signature (1, 9).