TL;DR
This paper investigates the critical loci within the moduli space of rank 2 Higgs bundles, focusing on the geometric and integrable system properties related to Higgs fields vanishing on divisors.
Contribution
It introduces a detailed analysis of the critical loci associated with Higgs fields vanishing on divisors and explores their induced integrable systems and geometric properties.
Findings
Characterization of critical loci as divisors where Higgs fields vanish
Establishment of an induced integrable system related to twisted Higgs bundles
Analysis of topological and differential-geometric properties of these loci
Abstract
The paper studies the locus in the rank 2 Higgs bundle moduli space corresponding to points which are critical for d of the Poisson commuting functions. These correspond to the Higgs field vanishing on a divisor of degree D. The degree D critical locus has an induced integrable system related to K(-D)-twisted Higgs bundles. Topological and differential-geometric properties of the critical loci are addressed.
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.