晶格Veech群的基本定义域和生成

IF 1.1 3区数学 Q1 MATHEMATICS

Commentarii Mathematici Helvetici Pub Date : 2017-01-01 DOI:10.4171/CMH/406

R. E. Mukamel

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引用次数: 20

摘要

非零格g二次微分的模空间QMg具有g D GL 2的自然作用，r /= 1 0 0 0 1。Veech集团PSL.X;q/是。x的稳定器;我们描述了一种寻找PSL.X元素的新算法;q/对于晶格Veech群，它可以用来计算基本域和生成器。利用我们的算法，我们首次给出了非算术Veech群的生成子和基本域的显式例子，其中H的属=PSL.X;Q /大于零。数学学科分类(2010)。32 g15, 30 + 30。

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Fundamental domains and generators for lattice Veech groups

The moduli space QMg of non-zero genus g quadratic differentials has a natural action of G D GL 2 .R/= ̋ ̇ 1 0 0 1 ̨ . The Veech group PSL.X; q/ is the stabilizer of .X; q/ 2 QMg in G. We describe a new algorithm for finding elements of PSL.X; q/ which, for lattice Veech groups, can be used to compute a fundamental domain and generators. Using our algorithm, we give the first explicit examples of generators and fundamental domains for non-arithmetic Veech groups where the genus of H=PSL.X; q/ is greater than zero. Mathematics Subject Classification (2010). 32G15, 30F30.

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来源期刊

Commentarii Mathematici Helvetici 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals. Commentarii Mathematici Helvetici is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.