Some aspects of the Hodge conjecture

Author: Voisin, Claire

Source: Japanese Journal of Mathematics, Volume 2, Number 2, September 2007 , pp. 261-296(36)

Publisher: Springer

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I will discuss positive and negative results on the Hodge conjecture. The negative aspects come on one side from the study of the Hodge conjecture for integral Hodge classes, and on the other side from the study of possible extensions of the conjecture to the general Kähler setting. The positive aspects come from algebraic geometry. They concern the structure of the so-called locus of Hodge classes, and of the Hodge loci.

Keywords: 14C30; 32J25; Chern classes; Hodge classes; Hodge loci

Document Type: Research Article


Affiliations: Institut de Mathématiques de Jussieu, CNRS UMR 7586, 175 rue du Chevaleret, 75103, Paris, France, Email:

Publication date: September 1, 2007

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