Tropical Homology

Ilia Itenberg, Ludmil Katzarkov, Grigory Mikhalkin, Ilia Zharkov

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2 Scopus citations


Given a tropical variety X and two non-negative integers p and q we define a homology group Hp,q(X) which is a finite-dimensional vector space over Q. 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 Hp,q(X) coincides with the Hodge number hp,q of a general member of the family.

Original languageEnglish (US)
Pages (from-to)963-1006
Number of pages44
JournalMathematische Annalen
Issue number1-2
StatePublished - Jun 1 2019


ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Itenberg, I., Katzarkov, L., Mikhalkin, G., & Zharkov, I. (2019). Tropical Homology. Mathematische Annalen, 374(1-2), 963-1006.