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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Log-concavity of the Duistermaat-Heckman measure for semifree Hamiltonian $S^1$-actions
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by Yunhyung Cho PDF
Proc. Amer. Math. Soc. 142 (2014), 2417-2428 Request permission

Abstract:

The Ginzberg-Knutson conjecture states that for any Hamiltonian Lie group $G$-action, the corresponding Duistermaat-Heckman measure is log- concave. It turns out that the conjecture is not true in general, but every well-known counterexample has non-isolated fixed points. In this paper, we prove that if the Hamiltonian circle action on a compact symplectic manifold $(M,\omega )$ is semifree and all fixed points are isolated, then the Duistermaat-Heckman measure is log-concave. With the same assumption, we also prove that $\omega$ and every reduced symplectic form satisfy the hard Lefschetz property.
References
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Additional Information
  • Yunhyung Cho
  • Affiliation: School of Mathematics, Korea Institute for Advanced Study (KIAS), 87 Hoegiro, Dongdaemun-gu, Seoul, 130-722, Republic of Korea
  • Email: yhcho@kias.re.kr
  • Received by editor(s): July 22, 2012
  • Published electronically: April 3, 2014

  • Dedicated: This paper is dedicated to my father
  • Communicated by: Lei Ni
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 2417-2428
  • MSC (2010): Primary 37J05, 53D20; Secondary 37J10
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12014-4
  • MathSciNet review: 3195764