The Poincare line bundle and autoduality of Hitchin fibers

TL;DR

This paper constructs the Poincare line bundle for Higgs bundles on smooth projective curves and demonstrates its role in inducing a fully-faithful Fourier-Mukai transform on quasi-coherent sheaves, revealing new duality properties.

Contribution

It introduces the Poincare line bundle for Higgs bundles and establishes its application in Fourier-Mukai transforms, advancing the understanding of autoduality of Hitchin fibers.

Findings

Construction of the Poincare line bundle for Higgs bundles

Proof that it induces a fully-faithful Fourier-Mukai transform

Implications for autoduality of Hitchin fibers

Abstract

In this paper we construct the Poincare line bundle for the stack of Higgs bundles on smooth projective curves and show that it induces a fully-faithful Fourier-Mukai transform on the category of quasi-coherent sheaves.