Japanese Journal of Mathematics

, Volume 2, Issue 2, pp 261–296

Some aspects of the Hodge conjecture

Special Feature: The 1st Takagi Lecture

DOI: 10.1007/s11537-007-0639-x

Cite this article as:
Voisin, C. Jpn. J. Math. (2007) 2: 261. doi:10.1007/s11537-007-0639-x

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 classesChern classesHodge loci

Mathematics Subject Classification (2000):

14C3032J25

Copyright information

© The Mathematical Society of Japan and Springer 2007

Authors and Affiliations

  1. 1.Institut de Mathématiques de JussieuCNRS UMR 7586ParisFrance