Tropical Homology

Abstract

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.

42 PAGES, 1 figure, introduction expanded and references added, publication status added

Cited by in corpus (3)

• Lefschetz (1,1)-theorem in tropical geometry
• Haas' theorem revisited
• Relations de Hodge--Riemann et combinatoire des matroïdes (d'après K. Adiprasito, J. Huh et E. Katz)