Automorphisms of surfaces of general type with $q\geq 2$ acting trivially in cohomology
Automorphisms of surfaces of general type with $q\geq 2$ acting trivially in cohomology
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DOI：
10.1112/s0010437x13007264
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发表时间：
2012-09
影响因子：
1.8
通讯作者：
J. Cai;Wenfei Liu;Lei Zhang
中科院分区：
文献类型：
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作者：
J. Cai;Wenfei Liu;Lei Zhang
摘要本文证明了具有不规则性的一般型曲面 $q\geq 3$ 是理性上同源刚性的吗，最小表面也是 $S$ 有 $q(S)= 2$ 除非 ${ K}_{S}^{2} = 8\chi ({ \mathcal{O} }_{S} )$． 这是一个曲面 $S$ 如果它的自同构群是理性上同构刚性的 $\mathrm{Aut} (S)$ 忠实地作用于上同环 ${H}^{\ast } (S, \mathbb{Q} )$． 作为例子，我们给出了一个完整的分类表面同质的产品与 $q(S)= 2$ 它们不是理性上同源僵化的。
Abstract In this paper we prove that surfaces of general type with irregularity $q\geq 3$ are rationally cohomologically rigidified, and so are minimal surfaces $S$ with $q(S)= 2$ unless ${ K}_{S}^{2} = 8\chi ({ \mathcal{O} }_{S} )$. Here a surface $S$ is said to be rationally cohomologically rigidified if its automorphism group $\mathrm{Aut} (S)$ acts faithfully on the cohomology ring ${H}^{\ast } (S, \mathbb{Q} )$. As examples we give a complete classification of surfaces isogenous to a product with $q(S)= 2$ that are not rationally cohomologically rigidified.