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.
On the Hodge conjecture for hypersurfaces in toric varieties / Bruzzo, Ugo; Grassi, Antonella. - In: COMMUNICATIONS IN ANALYSIS AND GEOMETRY. - ISSN 1019-8385. - 28:8(2020), pp. 1773-1786. [10.4310/CAG.2020.V28.N8.A1]
On the Hodge conjecture for hypersurfaces in toric varieties
Ugo Bruzzo
;
2020-01-01
Abstract
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.File in questo prodotto:
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