On rigid compact complex surfaces and manifolds
On rigid compact complex surfaces and manifolds
复制标题
在刚性紧凑的复杂表面和流形上
DOI：
10.1016/j.aim.2018.05.041
复制
发表时间：
2016
影响因子：
1.7
通讯作者：
F. Catanese
中科院分区：
文献类型：
--
作者：
I. Bauer;F. Catanese
本文研究刚性紧致复流形的问题。首先，我们研究了刚性的不同概念(局部刚性、全局刚性、无穷小刚性、整体刚性和强刚性)以及它们之间的关系。只有对于曲线，这些概念才重合，唯一的刚性曲线是投影线。对于曲面，我们证明了非极小一般类型的刚性曲面或者是≥5次的Del Pezzo曲面，或者是Inoue曲面。我们给出了n维≥3，Kodaira维0，2≤k≤n的刚性流形的例子.我们的主要定理是：完全四边形上分支的指数n≥4的HirzebruchKummer覆盖是无穷小刚性的.此外，我们提出了一些问题。
This article investigates the subject of rigid compact complex manifolds. First of all we investigate the different notions of rigidity (local rigidity, global rigidity, infinitesimal rigidity, etale rigidity and strong rigidity) and the relations among them. Only for curves these notions coincide and the only rigid curve is the projective line. For surfaces we prove that a rigid surface which is not minimal of general type is either a Del Pezzo surface of degree≥ 5 or an Inoue surface. We give examples of rigid manifolds of dimension n≥ 3 and Kodaira dimensions 0, and 2≤ k≤ n. Our main theorem is that the Hirzebruch Kummer coverings of exponent n≥ 4 branched on a complete quadrangle are infinitesimally rigid. Moreover, we pose a number of questions.