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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On singularities of primitive cohomology classes
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by Mark Andrea A. de Cataldo and Luca Migliorini
Proc. Amer. Math. Soc. 137 (2009), 3593-3600
DOI: https://doi.org/10.1090/S0002-9939-09-10014-X
Published electronically: June 18, 2009

Abstract:

Green and Griffiths have introduced several notions of singularities associated with normal functions, especially in connection with middle-dimensional primitive Hodge classes. In this paper, by using the more elementary aspects of the Decomposition Theorem, we define global and local singularities associated with primitive middle-dimensional cohomology classes, and by using the Relative Hard Lefschetz Theorem, we show that these singularities detect the global and local triviality of the primitive class.
References
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Bibliographic Information
  • Mark Andrea A. de Cataldo
  • Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794
  • Luca Migliorini
  • Affiliation: Dipartimento di Matematica, Università di Bologna, 40126 Bologna, Italy
  • MR Author ID: 248786
  • ORCID: 0000-0001-5145-0755
  • Received by editor(s): June 11, 2008
  • Received by editor(s) in revised form: February 12, 2009
  • Published electronically: June 18, 2009
  • Communicated by: Ted Chinburg
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 3593-3600
  • MSC (2000): Primary 14D06, 14D07
  • DOI: https://doi.org/10.1090/S0002-9939-09-10014-X
  • MathSciNet review: 2529865