On the Noether-Lefschetz theory in projective toric orbifolds

7 Oct 2025, 11:00
1h
Littoral Hotel

Littoral Hotel

João Pessoa, Brazil

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.

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