What is … a Hodge locus?

This page hosts information on Ananyo Dan's talk "What is … a Hodge locus?" at the "What is …?" seminar. The talk will take place on Friday, December 7, 5:30pm at HU, RUD 25 1.023.

Abstract

Given a family of smooth projective varieties B, the Hodge locus corresponding to a Hodge class \gamma parametrizes all b \in B where \gamma remains a Hodge class. In this talk we discuss the definition of a Hodge class, variation of Hodge structures and the statement of the Hodge conjecture. We also look at the Lefschetz (1,1)-theorem which states that the Hodge conjecture is true in the case of divisors.

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