Cohomology of the moduli of Higgs bundles and the Hausel-Thaddeus conjecture

Abstract: We describe the cohomological structure of the moduli space of stable SL_n Higgs bundles on a curve following the topological mirror symmetry conjecture of Hausel-Thaddeus. For the approach, we establish a connection between: (a) the moduli space of twisted Higgs bundles by an effective divisor of degree greater than 2g-2, and (b) the moduli space of K_C-Higgs bundles, using vanishing cycle functors. This allows us to apply Ngo's support theorem, which has a simpler form in the case (a) (by Ngo, Chaudouard-Laumon, de Cataldo), to the case of (b) which concerns hyper-Kähler geometries. In particular, this gives a new proof of the Hausel-Thaddeus conjecture proven previously by Gröchenig-Wyss-Ziegler via p-adic integrations. Based on joint work with Davesh Maulik.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

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