Degeneration of a graph describing conformal structure

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2023-01-01 DOI:10.4213/sm9703e

Andrei Borisovich Bogatyrev

引用次数: 1

Abstract

We consider the cell decomposition of the moduli space of real genus $2$ curves with marked point on the unique real oval. The cells are enumerated by certain graphs, whose weights describe the complex structure on the curve. We show that the collapse of an edge in a graph results in a root-like singularity of the natural map from the weights on graphs to the moduli space of curves. Bibliography: 24 titles.

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描述共形结构的图的退化

考虑了唯一实数椭圆上有标记点的实2元曲线模空间的单元分解。单元格由特定的图来枚举，这些图的权重描述了曲线上的复杂结构。我们证明了图中一条边的坍缩会导致从图的权值到曲线的模空间的自然映射的类根奇异性。参考书目:24篇。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis