An extension of the Noether-Lefschetz loci in toric varieties

Abstract: In this talk, I will motivate and prove a Noether-Lefschetz type theorem for quasi-smooth intersections in a projective simplicial toric variety with suitable conditions, which implies that the Hodge conjecture holds on a very general quasi-smooth intersection variety and that the natural extension of the Noether-Lefchetz loci is not empty. The Noether-Lefschetz loci can be understood as the loci where the Hodge conjecture is unknown. If time allows me, I will also show that the Hodge conjecture is also true for some varieties in the Noether-Lefschetz loci. This is joint work with Prof. Ugo Bruzzo.

algebraic geometry

Audience: researchers in the topic

Brazilian algebraic geometry seminar

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Previous talks available at the YouTube channel "Brazilian Algebraic Geometry" www.youtube.com/channel/UCM-pcdNdpWxQFgOg-illE2w