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Article Dans Une Revue Mathematische Annalen Année : 2019

Tropical Homology

Résumé

Given a tropical variety X and two non-negative integers p and q we define homology group $H_{p,q}(X)$. We show that if X is a smooth tropical variety that can be represented as the tropical limit of a 1-parameter family of complex projective varieties, then $\dim H_{p,q}(X)$ coincides with the Hodge number $h^{p,q}$ of a general member of the family.

Dates et versions

hal-03983044 , version 1 (10-02-2023)

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Ilia Itenberg, Ludmil Katzarkov, Grigory Mikhalkin, Ilia Zharkov. Tropical Homology. Mathematische Annalen, 2019. ⟨hal-03983044⟩
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