Abstract
In 2012 Bruzzo and Grassi proved a version of the Noether-Lefschetz Theorem for toric varieties, claiming that, on a very general quasi-smooth hypersurface X of an odd-dimensional projective simplicial toric Oda variety, with degree big enough, the (k,k)-cohomology classes of X come from the ambient space. The Noether-Lefschetz locus is the locus of quasi-smooth hypersurfaces with a fixed…