Tropical Homology - Archive ouverte HAL Access content directly
Journal Articles Mathematische Annalen Year : 2019

Tropical Homology


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 and versions

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



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



Gmail Facebook Twitter LinkedIn More