Surfaces of general type with q = 2 are rigidified
Surfaces of general type with q = 2 are rigidified
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DOI：
10.1142/s0219199717500845
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发表时间：
2015-05
影响因子：
1.6
通讯作者：
Wenfei Liu
中科院分区：
文献类型：
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作者：
Wenfei Liu
设[Formula：see text]是一般类型的极小光滑射影曲面，具有不规则性[Formula：see text]。我们证明，如果[公式：见正文]有一个非平凡的全纯自同构平凡地作用于有理系数的上同调，那么它是一个与乘积同构的曲面。作为这种几何特征的结果，人们推断，没有非平凡的自同构曲面的一般类型与[公式：见文字]（这不一定是最小的）可以同伦的身份。特别地，这样的表面在Fabrizio Catanese的意义上被硬化。
Let [Formula: see text] be a minimal smooth projective surface of general type with irregularity [Formula: see text]. We show that, if [Formula: see text] has a nontrivial holomorphic automorphism acting trivially on the cohomology with rational coefficients, then it is a surface isogenous to a product. As a consequence of this geometric characterization, one infers that no nontrivial automorphism of surfaces of general type with [Formula: see text] (which are not necessarily minimal) can be homotopic to the identity. In particular, such surfaces are rigidified in the sense of Fabrizio Catanese.