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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Hitchin fibrations, abelian surfaces, and the P=W conjecture
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by Mark Andrea de Cataldo, Davesh Maulik and Junliang Shen HTML | PDF
J. Amer. Math. Soc. 35 (2022), 911-953 Request permission


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.

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Additional Information
  • Mark Andrea de Cataldo
  • Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, USA
  • MR Author ID: 291970
  • Email:
  • Davesh Maulik
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge MA 02138, USA
  • MR Author ID: 672937
  • Email:
  • Junliang Shen
  • Affiliation: Department of Mathematics, Yale University, 442 Dunham Lab, 10 Hillhouse Ave., New Haven, CT 06511, USA
  • MR Author ID: 1134436
  • Email:
  • Received by editor(s): October 3, 2019
  • Received by editor(s) in revised form: June 4, 2021
  • Published electronically: November 2, 2021
  • Additional Notes: The first author was partially supported by NSF grants DMS 1600515 and 1901975.
    The second author was partially supported by NSF FRG grant DMS-1159265.
    The third author was supported by the NSF grant DMS 2134315.
  • © Copyright 2021 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 35 (2022), 911-953
  • MSC (2020): Primary 14H60, 14F45, 14D20
  • DOI:
  • MathSciNet review: 4433080