Workshop: Motives of moduli spaces of Higgs bundles

Date: 2021-10-19

Time: 11:00 - 12:00

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Victoria Hoskins


In joint work with Simon Pepin Lehalleur, we show the motive of the moduli space of stable Higgs bundles with coprime invariants on a curve is generated by the motive of the curve. Our geometric strategy starts with Hitchin’s scaling action on the Higgs moduli space, which we use to show this motive is pure. We use this scaling action together with Harder–Narasimhan recursions and variation of stability for moduli stacks of chains following work of García-Prada, Heinloth and Schmitt to show the motive of the Higgs moduli space is a direct factor of the motive of a sufficiently large power of the curve. We also use this scaling action to prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic, and thus have isomorphic Chow rings.