Constructing algebraic cycles on hypersurfaces, an explicit approach to Hodge conjecture

Abstract: Hodge conjecture is one of the major conjectures in algebraic geometry. In all the cases where Hodge conjecture has been verified, no constructive proof has been given up to the date. In other words there is no hint about how to construct an algebraic cycle from a given Hodge cycle. In this talk we will consider this problem in the case of hypersurfaces of the projective space. We will explain how this question becomes more treatable when the Hodge cycle is given in a good enough format in terms of Griffiths basis. Reducing the problem to constructing these nice representatives of Hodge cycles. We will see some examples where this approach works and highlight the difficulties that appear in the general case.

algebraic geometry

Audience: researchers in the topic

Brazilian algebraic geometry seminar

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