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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Variational Hodge conjecture and Hodge loci

## Variational Hodge conjecture and Hodge lociAdd to your list(s) Download to your calendar using vCal - Hossein Movasati (IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro)
- Thursday 23 January 2020, 11:15-12:15
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. KAH - K-theory, algebraic cycles and motivic homotopy theory Grothendieck’s variational Hodge conjecture (VHC) claims that if we have a continuous family of Hodge cycles (flat section of the Gauss-Manin connection) and the Hodge conjecture is true at least for one Hodge cycle of the family then it must be true for all such Hodge cycles. A stronger version of this (Alternative Hodge conjecture, AHC ), asserts that the deformation of an algebraic cycle Z togther with the projective variety X, where it lives, is the same as the deformation of the cohomology class of Z in X. There are many simple counterexamples to AHC , however, in explict situations, like algebraic cycles inside hypersurfaces, it becomes a challenging problem. In this talk I will review few cases in which AHC is true (including Bloch's semi-regular and local complete intersection algebraic cycles) and other cases in which it is not true. The talk is mainly based on the article arXiv:1902.00831. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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