Stratifications on the Moduli Space of Higgs Bundles
Peter B. Gothen, Ronald A. Z\'u\~niga-Rojas
TL;DR
This paper investigates the relationship between two stratifications of the moduli space of rank three Higgs bundles, expanding understanding beyond the rank two case where they coincide.
Contribution
It provides a detailed analysis of how the Bialynicki-Birula and Shatz stratifications differ in higher rank Higgs bundles, specifically for rank three.
Findings
The two stratifications do not coincide in rank three.
The paper characterizes the differences between the stratifications.
Insights into the structure of the moduli space for higher rank Higgs bundles.
Abstract
The moduli space of Higgs bundles has two stratifications. The Bialynicki-Birula stratification comes from the action of the non-zero complex numbers by multiplication on the Higgs field, and the Shatz stratification arises from the Harder-Narasimhan type of the vector bundle underlying a Higgs bundle. While these two stratification coincide in the case of rank two Higgs bundles, this is not the case in higher rank. In this paper we analyze the relation between the two stratifications for the moduli space of rank three Higgs bundles.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.