Estratifica\c{c}\~oes no espa\c{c}o m\'oduli dos fibrados de Higgs

TL;DR

This paper explores the relationship between two stratifications of the moduli space of Higgs bundles, extending known results from rank two to rank three, and provides a classification approach for the latter.

Contribution

It offers a new approach to classify the Shatz stratification in rank three Higgs bundles using the Bialynicki-Birula stratification.

Findings

Rank two stratification results are extended to rank three.

A classification method for the Shatz stratification in rank three is proposed.

The relationship between two stratifications is clarified in higher rank cases.

Abstract

The work of Hausel proves that the Bialynicki-Birula stratification of the moduli space of rank two Higgs bundles coincides with its Shatz stratification. These two stratifications do not coincide in general. Here, we give an approach for the rank three case of the classification of the Shatz stratification in terms of the Bialynicki-Birula stratification.