具有阿贝尔Beauville群的Beauville曲面
代数几何
2012-03-15 v3 群论
摘要
Beauville曲面是一类刚性的一般型曲面，它由亏格g1,g2≥2的曲线C1,C2的乘积通过有限群G的自由作用商得到。本文研究G为阿贝尔群（根据Catanese的结果，此时G≅Z_n^2且gcd(n,6)=1）的Beauville曲面。对于每个这样的n，我们能够描述所有此类曲面，给出其同构类数量的公式，并确定它们可能的自同构群。这一显式描述还使我们能够观察到这些曲面均在Q上定义。
引用
@article{arxiv.1102.4552,
title = {Beauville surfaces with abelian Beauville group},
author = {Gabino González-Diez and Gareth A. Jones and David Torres-Teigell},
journal= {arXiv preprint arXiv:1102.4552},
year = {2012}
}
备注
14 pages. This version contains amended references to related work of Garion and Penegini, who have recently replaced their paper arXiv:0910.5402v1 with arXiv:0910.5402v3 and arXiv:1107.5534, the latter resolving certain discrepancies between their results and ours