Hitchin fibrations, abelian surfaces, and the P=W conjecture

By M. A. Cataldo, Davesh Maulik, Junliang Shen. 2019

54 citations recorded by the source corpus.

We study the topology of Hitchin fibrations via abelian surfaces. We establish the P=W conjecture for genus $2$ curves and arbitrary rank. In higher genus and arbitrary rank, we prove that P=W holds for the subalgebra of cohomology generated by even tautological classes. Furthermore, we show that all tautological generators lie in the correct pieces of the perverse filtration as predicted by the P=W conjecture. In combination with recent work of Mellit, this reduces the full conjecture to the multiplicativity of the perverse filtration. Our main technique is to study the Hitchin fibration as a degeneration of the Hilbert-Chow morphism associated with the moduli space of certain torsion sheaves on an abelian surface, where the symmetries induced by Markman's monodromy operators play a crucial role.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/58f3f2cb473430e7981359e1e484b44df9f18eaf

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Cohomological χ–independence for moduli of one-dimensional sheaves and moduli of Higgs bundles (2020, background): “For other places where GV invariants arise geometrically, see [47] and [9] for connections with hyper-Kähler geometries and the P = W conjecture [4, 6] respectively.”