Hitchin fibrations, abelian surfaces, and the P=W conjecture
Author(s)
de Cataldo, Mark; Maulik, Davesh; Shen, Junliang
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<p>We study the topology of Hitchin fibrations via abelian surfaces. We establish the P=W conjecture for genus <inline-formula content-type="math/mathml">
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</inline-formula> 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.</p>
<p>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.</p>
Date issued
2021-11-02Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Journal of the American Mathematical Society
Publisher
American Mathematical Society (AMS)
Citation
de Cataldo, Mark, Maulik, Davesh and Shen, Junliang. 2021. "Hitchin fibrations, abelian surfaces, and the P=W conjecture." Journal of the American Mathematical Society, 35 (3).
Version: Final published version