The Automorphism Equivariant Hitchin Index
Differential Geometry
2025-11-18 v2 Algebraic Geometry
Abstract
Let T be the one-dimensional complex torus. We consider the action of an automorphism of a Riemann surface X on the cohomology of the T-equivariant determinant line bundle over the moduli space of rank two Higgs bundles on X with fixed determinant of odd degree. We define and study the automorphism equivariant Hitchin index. We prove a formula for it in terms of cohomological pairings of canonical T-equivariant classes of certain moduli spaces of parabolic Higgs bundles over the quotient Riemann surface.
Cite
@article{arxiv.2401.13289,
title = {The Automorphism Equivariant Hitchin Index},
author = {Jørgen Ellegaard Andersen and William Elbæk Mistegård},
journal= {arXiv preprint arXiv:2401.13289},
year = {2025}
}