On the Hodge conjecture for hypersurfaces in toric varieties

Ugo Bruzzo; Antonella Grassi

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arXiv · 1708.04944

On the Hodge conjecture for hypersurfaces in toric varieties

Ugo Bruzzo·Antonella Grassi

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Abstract

We show that very general hypersurfaces in odd-dimensional simplicial projective toric varieties verifying a certain combinatorial property satisfy the Hodge conjecture (these include projective spaces). 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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Ugo Bruzzo, Antonella Grassi. 2017-08-16. On the Hodge conjecture for hypersurfaces in toric varieties. https://arxiv.org/abs/1708.04944

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