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摘要翻译：
经典的McKay对应从SU(2)的有限子群G的表示理论和G的仿射平面商的最小分辨率几何中建立了一个显式的联系。本文讨论了McKay对应在G被SU(1,1）的泛覆盖的一个共紧离散子群代替时的一个可能的推广，使得它在PSU(1,1）中的像是亏格商为0的共紧fuchsian群。我们建立了开代数曲面上G的一类有限维酉表示与向量丛之间的对应关系，并给出了与G正则相关的平凡正则类。
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英文标题：
《McKay's correspondence for cocompact discrete subgroups of SU(1,1)》
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作者：
Igor V. Dolgachev
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Geometric Topology 几何拓扑
分类描述：Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
流形，轨道，多面体，细胞复合体，叶状，几何结构
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英文摘要：
The classical McKay correspondence establishes an explicit link from the representation theory of a finite subgroup G of SU(2) and the geometry of the minimal resolution of the quotient of the affine plane by G. In this paper we discuss a possible generalization of the McKay correspondence to the case when G is replaced with a cocompact discrete subgroup of the universal cover of SU(1,1) such that its image in PSU(1,1) is a cocompact fuchsian group with quotient of genus 0. We establish a correspondence between a certain class of finite-dimensional unitary representations of G and vector bundles on an open algebraic surface with the trivial canonical class canonically associated to G.
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PDF链接：
https://arxiv.org/pdf/0710.2253
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