Fractional Dehn twists and modular invariants

TL;DR

This paper explores the connection between fractional Dehn twist coefficients of surface automorphisms and modular invariants of algebraic curves, providing characterizations and bounds for pseudo-periodic maps.

Contribution

It establishes a relationship between fractional Dehn twists and modular invariants, offering new characterizations and bounds for pseudo-periodic maps.

Findings

Characterization of pseudo-periodic maps with nontrivial fractional Dehn twists

Uniform lower bounds for non-zero fractional Dehn twist coefficients

Link between Dehn twists and modular invariants

Abstract

In this note, we establish a relationship between fractional Dehn twist coefficients of Riemann surface automorphisms and modular invariants of holomorphic families of algebraic curves. Specially, we give a characterization of pseudo-periodic maps with nontrivial fractional Dehn twist coefficients. We also obtain some uniform lower bounds of non-zero fractional Dehn twist coefficients.