The fine structure of Kontsevich-Zorich strata for genus 3

TL;DR

This paper characterizes the structure of Kontsevich-Zorich strata in genus 3 using root system data and provides presentations of their orbifold fundamental groups for non-open strata.

Contribution

It offers a detailed description of genus 3 strata and explicit fundamental group presentations, advancing understanding of their geometric and topological properties.

Findings

Stratification of genus 3 moduli space described via root systems

Explicit orbifold fundamental group presentations for non-open strata

Enhanced understanding of the geometric structure of Kontsevich-Zorich strata

Abstract

We give a description of the Kontsevich-Zorich strata for genus 3 in terms of root system data. For each non-open stratum we obtain a presentation of its orbifold fundamental group.