Topological mirror symmetry for parabolic Higgs bundles

Abstract

We prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli space of strongly parabolic Higgs bundles of rank two or three, with full flags. Although the main theorem is proved only for rank at most three, most of the results are proved for any prime rank.

37 pages; minor changes. Final version: to appear in J. Geom. Phys

References in corpus (9)

• Mirror Symmetry is T-Duality
• A New Cohomology Theory for Orbifold
• Lectures on Special Lagrangian Submanifolds
• Mirror symmetry, Langlands duality, and the Hitchin system
• Stringy Hodge numbers of varieties with Gorenstein canonical singularities
• Moduli Spaces of Parabolic Higgs Bundles and Parabolic K(D) Pairs over Smooth Curves: I
• Orbifold Riemann Surfaces and the Yang-Mills-Higgs Equations
• Examples of mirror partners arising from integrable systems
• SYZ duality for parabolic Higgs moduli spaces

Cited by in corpus (9)

• Unramified covers and branes on the Hitchin system
• Serre polynomials of $S{L}_n$- and $PG{L}_n$-character varieties of free groups
• Aspects of the topology and combinatorics of Higgs bundle moduli spaces
• Higgs bundles, Lagrangians and mirror symmetry
• Mirror symmetry for parabolic Higgs bundles via $p$-adic integration
• Monodromy of Rank 2 Parabolic Hitchin Systems
• Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study
• Tame parahoric nonabelian Hodge correspondence on curves
• Motivic mirror symmetry and $\chi$-independence for Higgs bundles in arbitrary characteristic