Author:
Groechenig Michael,Wyss Dimitri,Ziegler Paul
Abstract
AbstractWe prove the Topological Mirror Symmetry Conjecture by Hausel–Thaddeus for smooth moduli spaces of Higgs bundles of type $$SL_n$$
S
L
n
and $$PGL_n$$
P
G
L
n
. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore, we prove for d prime to n, that the number of rank n Higgs bundles of degree d over a fixed curve defined over a finite field, is independent of d. This proves a conjecture by Mozgovoy–Schiffmann in the coprime case.
Funder
Technische Universität München
Publisher
Springer Science and Business Media LLC
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