Speaker
William D. Montoya
(Universidade Estadual de Campinas, Brazil)
Description
In 2012, Bruzzo and Grassi proved a Noether-Lefschetz theorem for toric varieties, which claims that for a (2k+1)-dimensional projective toric orbifold with suitable conditions on a very general quasi-smooth hypersurface $X$, each $(k,k)$-cohomology class on $X$ comes from the ambient toric variety. The Noether-Lefschetz locus is the locus of quasi-smooth hypersurfaces with the same degree such that there exists a $(k,k)$-cohomology class that does not come from the ambient toric variety. In this talk, I will present the main results about the Noether-Lefschetz loci in toric varieties based on my joint work with Prof. Ugo Bruzzo in recent years.