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Mathematics Colloquium

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Date:  Tuesday, April 07, 2015

Title:  A tropical approach to a Hodge conjecture for positive currents

Abstract:  Demailly showed that the Hodge conjecture is equivalent to the statement that any closed (p,p)-dimensional current with rational cohomology class can be approximated by linear combinations of algebraic subvarieties, and asked whether any positive closed (p,p)-dimensional current with rational cohomology class can be approximated by positive linear combinations of algebraic subvarieties. Using tropical geometry, we construct a positive closed (p,p)-dimensional current on a smooth projective variety that does not satisfy the latter statement. This is a joint work with Farhad Babaee.


Speaker:  June Huh
Institution:  Princeton University

 

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