摘要翻译:
作为主要结果,我们证明了对于每一个g>1,亏格g存在一些平移曲面,其Veech群是SL(2,Z)的非同余子群。我们使用Origamis/方形平铺曲面来生成我们的示例。本文分为两个部分:第一部分介绍了平移曲面、origamis、Veech群和Teichmueller曲线,并证明了2属中的两个origamis的Veech群是非同余群;在第二部分中,我们提供了一种产生Veech群减少的origamis序列的技术。这是用来证明主要结果。
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英文标题:
《Origamis with non congruence Veech groups》
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作者:
Gabriela Schmithuesen
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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: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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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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英文摘要:
As main result we show that for each g > 1 there is some translation surface of genus g whose Veech group is a non congruence subgroup of SL(2,Z). We use origamis/square-tiled surfaces to produce our examples. The article is divided into two parts: In the first part we introduce translation surfaces, origamis, Veech groups and Teichmueller curves and show for two origamis in genus 2 that their Veech groups are non congruence groups; in the second part we provide a technique that produces sequences of origamis whose Veech groups are decreasing. This is used to prove the main result.
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PDF链接:
https://arxiv.org/pdf/0704.0416