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Article Dans Une Revue Annales Henri Lebesgue Année : 2021

Lefschetz section theorems for tropical hypersurfaces

Résumé

We establish variants of the Lefschetz section theorem for the integral tropical homology groups of tropical hypersurfaces of tropical toric varieties. It follows from these theorems that the integral tropical homology groups of non-singular tropical hypersurfaces which are compact or contained in Rn are torsion free. We prove a relationship between the coefficients of the χy genera of complex hypersurfaces in toric varieties and Euler characteristics of the integral tropical cellular chain complexes of their tropical counterparts. It follows that the integral tropical homology groups give the Hodge numbers of compact non-singular hypersurfaces of complex toric varieties. Finally for tropical hypersurfaces in certain affine toric varieties, we relate the ranks of their tropical homology groups to the Hodge–Deligne numbers of their complex counterparts.

Dates et versions

hal-04393637 , version 1 (14-01-2024)

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Citer

Charles Arnal, Arthur Renaudineau, Kris Shaw. Lefschetz section theorems for tropical hypersurfaces. Annales Henri Lebesgue, 2021, 4, pp.1347-1387. ⟨10.5802/ahl.104⟩. ⟨hal-04393637⟩
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