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On the Hodge conjecture for hypersurfaces in toric varieties
Communications in Analysis and Geometry  (IF0.736),  Pub Date : 2021-01-08, DOI: 10.4310/cag.2020.v28.n8.a1
Ugo Bruzzo, Antonella Grassi

We show that for very general hypersurfaces in odd-dimensional simplicial projective toric varieties satisfying an effective combinatorial property the Hodge conjecture holds. This gives a connection between the Oda conjecture and Hodge conjecture. We also give an explicit criterion which depends on the degree for very general hypersurfaces for the combinatorial condition to be verified.