Saturated orbit closures in the Hodge bundle

TL;DR

This paper provides a new proof for classifying saturated orbit closures in the Hodge bundle's absolute period foliation, simplifying previous classifications through deformations of flat pairs of pants.

Contribution

It introduces a novel approach using deformations of flat pairs of pants to classify ${ m GL}^+(2, eal)$-orbit closures in the Hodge bundle.

Findings

Simplified proof of orbit closure classification

New method using flat pairs of pants deformations

Enhanced understanding of absolute period foliation

Abstract

We give a new proof of the classification of ${\rm GL}^+(2,\mathbb{R})$-orbit closures that are saturated for the absolute period foliation of the Hodge bundle. As a consequence, we obtain a short proof of the classification of closures of leaves of the absolute period foliation of the Hodge bundle. Our approach is based on a method for classifying ${\rm GL}^+(2,\mathbb{R})$-orbit closures using deformations of flat pairs of pants.