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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On singularities of primitive cohomology classes


Authors: Mark Andrea A. de Cataldo and Luca Migliorini
Journal: Proc. Amer. Math. Soc. 137 (2009), 3593-3600
MSC (2000): Primary 14D06, 14D07
Published electronically: June 18, 2009
MathSciNet review: 2529865
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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.


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Additional 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

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10014-X
PII: S 0002-9939(09)10014-X
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.