Automorphism groups of compact Riemann surfaces of genera three and four
Automorphism groups of compact Riemann surfaces of genera three and four
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三属和四属紧黎曼曲面的自同构群
DOI：
10.1016/0022-4049(90)90107-s
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发表时间：
1990
影响因子：
0.8
通讯作者：
Akikazu Kuribayashi
中科院分区：
文献类型：
--
作者：
I. Kuribayashi;Akikazu Kuribayashi
如何研究紧化黎曼曲面X的自同构群？我们认为它们与GL （g， C）中的基团一致。其中g（≥2）为X的属。X的自同构群AG可以表示为GL （g， C）的子群R （X， AG）。我们的主要目标是R （X， AG）的GL (g， C)-共轭类的分类。为了做到这一点，我们将RH， CY和ex条件应用于GL （g， C）的子群，并检查该群是否满足这些条件。这样，我们就得到了g= 3和4的自同构群的完全分类。
How do we investigate automorphism groups of a compact Riemann surface X? We consider them identified with the groups in GL (g, C). Here g (≥ 2) is the genus of X. A group AG of automorphisms of X can be represented as a subgroup R (X, AG) of GL (g, C). Our main target is the classification of the GL (g, C)-conjugate classes of R (X, AG). In order to do that, we apply the RH, the CY, and the EX-condition to a subgroup of GL (g, C) and check up on whether the group satisfies these conditions or not. In this way, we have a complete classification of the automorphism groups for g= 3and4.