On singularities of primitive cohomology classes

de Cataldo, Mark; Migliorini, Luca

doi:10.1090/S0002-9939-09-10014-X

On singularities of primitive cohomology classes
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by Mark Andrea A. de Cataldo and Luca Migliorini PDF

Proc. Amer. Math. Soc. 137 (2009), 3593-3600 Request permission

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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