We show that for very general hypersurfaces in odd-dimensional simplicial projective toric varieties satisfying an effective combina- torial 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.

ON THE HODGE CONJECTURE FOR HYPERSURFACES IN TORIC VARIETIES

Grassi Antonella;
2020

Abstract

We show that for very general hypersurfaces in odd-dimensional simplicial projective toric varieties satisfying an effective combina- torial 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/788442
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