Special Feature: The 1st Takagi Lecture

Japanese Journal of Mathematics

, Volume 2, Issue 2, pp 261-296

Some aspects of the Hodge conjecture

  • Claire VoisinAffiliated withInstitut de Mathématiques de Jussieu, CNRS UMR 7586 Email author 

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Abstract.

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 and Phrases:

Hodge classes Chern classes Hodge loci

Mathematics Subject Classification (2000):

14C30 32J25