On the sharp lower bounds of modular invariants and fractional Dehn twist coefficients-Reference-Cited by-同舟云学术

On the sharp lower bounds of modular invariants and fractional Dehn twist coefficients

Published:2022-04-20 Issue:787 Volume:2022 Page:163-195
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Liu Xiao-Lei¹,Tan Sheng-Li²

Affiliation:

1. School of Mathematical Sciences , Dalian University of Technology , Dalian , Liaoning Province , P. R. China

2. School of Mathematical Sciences , Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice , East China Normal University , Shanghai , P. R. China

Abstract

Abstract Modular invariants of families of curves are Arakelov invariants in arithmetic algebraic geometry. All the known uniform lower bounds of these invariants are not sharp. In this paper, we aim to give explicit lower bounds of modular invariants of families of curves, which is sharp for genus 2. According to the relation between fractional Dehn twists and modular invariants, we give the sharp lower bounds of fractional Dehn twist coefficients and classify pseudo-periodic maps with minimal coefficients for genus 2 and 3 firstly. We also obtain a rigidity property for families with minimal modular invariants, and other applications.

Funder

National Key Research and Development Program of China

National Natural Science Foundation of China

Fundamental Research Funds of the Central Universities

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2022-0014/pdf

Reference38 articles.

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4. A. Beauville, Le nombre minimum de fibres singulières d’une courbe stable sur ℙ1{\mathbb{P}}^{1}, Séminaire sur les pinceaux de courbes de genre au moins deux Astérisque 86, Société Mathématique de France, Paris (1981), 97–108.

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