台球和Teichmüller曲线

IF 2 3区数学 Q1 MATHEMATICS

Bulletin of the American Mathematical Society Pub Date : 2022-11-28 DOI:10.1090/bull/1782

C. McMullen

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引用次数: 5

摘要

Teichmüller曲线V⊂M g V\subet\mathcal{M}_g是黎曼曲面模空间中的等距浸入代数曲线。这些罕见的极端物体与多边形中的台球、霍奇理论、代数几何和表面拓扑有关。本文介绍了在过去30年中发现的六个已知的原始Teichmüller曲线族，以及一些悬而未决的问题。

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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Billiards and Teichmüller curves

A Teichmüller curve V ⊂ M g V \subset \mathcal {M}_g is an isometrically immersed algebraic curve in the moduli space of Riemann surfaces. These rare, extremal objects are related to billiards in polygons, Hodge theory, algebraic geometry and surface topology. This paper presents the six known families of primitive Teichmüller curves that have been discovered over the past 30 years, and a selection of open problems.

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来源期刊

Bulletin of the American Mathematical Society 数学-数学

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.