Orientations and Geometrisations of Compact Complex Surfaces
Orientations and Geometrisations of Compact Complex Surfaces
复制标题
紧凑复杂表面的方向和几何形状
DOI：
10.1112/s0024609396002287
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发表时间：
1997
影响因子：
0.9
通讯作者：
D. Kotschick
中科院分区：
文献类型：
--
作者：
D. Kotschick
每一个复流形都有一个正则方向，很自然地，我们会想知道底层的拓扑流形或光滑流形何时会有一个与另一个方向相容的复杂结构。Beauville在[2]中对紧致复曲面提出了这个问题。他指出，有很多例子，如曲线的乘积或霍普夫曲面，其中底层流形允许方向反转自同构。这意味着签名为零。Beauville问是否有非零签名的例子。1991年数学学科分类14J99、53C55、53C15。
Every complex manifold carries a canonical orientation, and it is natural to wonder when the underlying topological or smooth manifold carries a complex structure compatible with the other orientation. In [2], Beauville raised this question for compact complex surfaces. He noted that there are a lot of examples, like products of curves, or Hopf surfaces, where the underlying manifold admits an orientation‐reversing selfdiffeomorphism. This implies that the signature is zero. Beauville asked if there are any examples of non‐zero signature. 1991 Mathematics Subject Classification 14J99, 53C55, 53C15.