The birational geometry of irregular Higgs bundles

TL;DR

This paper explores the birational geometry of irregular Higgs bundles, establishing a Poisson isomorphism between moduli spaces and Picard bundles, advancing understanding of their geometric structures.

Contribution

It introduces a variant of the BNR correspondence for irregular parabolic Higgs bundles, linking moduli spaces with Picard bundles of ruled surface families.

Findings

Establishes a Poisson isomorphism between irregular Dolbeault moduli spaces and Picard bundles.

Provides a new perspective on the geometry of irregular Higgs bundles.

Extends classical correspondences to irregular and parabolic cases.

Abstract

We give a variant of the Beauville--Narasimhan--Ramanan correspondence for irregular parabolic Higgs bundles with semi-simple irregular part and show that it defines a Poisson isomorphism between certain irregular Dolbeault moduli spaces of a curve and relative Picard bundles of families of ruled surfaces over a curve.