Real normalized differentials and compact cycles in the moduli space of curves

TL;DR

This paper establishes a new upper bound on the dimension of complete subvarieties in the moduli space of curves using Whitham perturbation theory, advancing understanding of the geometric structure of these spaces.

Contribution

It introduces a novel application of Whitham perturbation theory to derive a sharp upper bound on subvariety dimensions in the moduli space of curves.

Findings

Proves an upper bound of 3g/2 - 2 for the dimension of complete subvarieties.

Utilizes constructions from integrable systems and Whitham theory.

Provides new insights into the geometry of the moduli space of curves.

Abstract

Using constructions of the Whitham perturbation theory of integrable system we prove a new sharp upper bound of $3g/2-2$ on the dimension of complete subvarieties of $\M_g^{ct}$.