Trace field degrees of Abelian differentials

TL;DR

This paper demonstrates that for every even number within a specific range, there exists a Thurston-Veech pseudo-Anosov stretch factor with that degree in all connected components of all strata of Abelian differentials.

Contribution

It establishes the realization of all even degrees within a range as stretch factor degrees across all strata of Abelian differentials.

Findings

Every even number 2 ≤ 2d ≤ 2g is realized as a stretch factor degree.

The result holds for all connected components of all strata.

Provides a comprehensive understanding of degree realizations in moduli spaces.

Abstract

We prove that every even number $2 \le 2d \le 2g$ is realised as the degree of a Thurston-Veech pseudo-Anosov stretch factor in every connected component of every stratum of the moduli space of Abelian differentials.