Variational Hodge conjecture and Hodge loci
Duration: 1 hour 5 mins
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About this item
| Description: |
Movasati, H
Thursday 23rd January 2020 - 11:15 to 12:15 |
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| Created: | 2020-02-03 12:38 |
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| Collection: | K-theory, algebraic cycles and motivic homotopy theory |
| Publisher: | Isaac Newton Institute |
| Copyright: | Movasati, H |
| Language: | eng (English) |
| Abstract: | 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. |
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