A characterization of Inoue surfaces with p(g)=0 and K-2=7
A characterization of Inoue surfaces with p(g)=0 and K-2=7
复制标题
p(g)=0 且 K-2=7 时 Inoue 表面的表征
DOI：
10.1007/s10711-018-0321-x
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发表时间：
2018
影响因子：
0.5
通讯作者：
Shin YongJoo
中科院分区：
文献类型：
--
作者：
Chen Yifan;Shin YongJoo
Inoue用和构造了第一个一般类型的光滑极小复曲面的例子.这些表面是有限的伽罗瓦覆盖的4节点三次曲面与伽罗瓦群，克莱因群。对于这样的曲面S，S的双正则映射的度为2，并且它在Galois群中仅由一个对合构成。该对合的固定轨迹的可除部分由两个不可约部分组成：一个是自交数为0的亏格3曲线，另一个是自交数为0的亏格2曲线.反之，设S是一般型的光滑极小复曲面，且有对合。我们证明了，如果的固定轨迹的整除部分由两个不可约分量组成，且，且，则Klein群忠实地作用在，且的确是Inoue曲面。
Inoue constructed the first examples of smooth minimal complex surfaces of general type withand. These surfaces are finite Galois covers of the 4-nodal cubic surface with the Galois group, the Klein group. For such a surfaceS, the bicanonical map ofShas degree 2 and it is composed with exactly one involution in the Galois group. The divisorial part of the fixed locus of this involution consists of two irreducible components: one is a genus 3 curve with self-intersection number 0 and the other is a genus 2 curve with self-intersection number. Conversely, assume thatSis a smooth minimal complex surface of general type with,and having an involution. We show that, if the divisorial part of the fixed locus ofconsists of two irreducible componentsand, withand, then the Klein groupacts faithfully onSandSis indeed an Inoue surface.