Tropical Homology

Ilia Itenberg, Ludmil Katzarkov, Grigory Mikhalkin, Ilia Zharkov

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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

Original languageEnglish (US)
Pages (from-to)1-44
Number of pages44
JournalMathematische Annalen
DOIs
StateAccepted/In press - May 26 2018

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Homology
Homology Groups
Projective Variety
Vector space
Non-negative
Integer
Family

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Itenberg, I., Katzarkov, L., Mikhalkin, G., & Zharkov, I. (Accepted/In press). Tropical Homology. Mathematische Annalen, 1-44. https://doi.org/10.1007/s00208-018-1685-9

Tropical Homology. / Itenberg, Ilia; Katzarkov, Ludmil; Mikhalkin, Grigory; Zharkov, Ilia.

In: Mathematische Annalen, 26.05.2018, p. 1-44.

Research output: Contribution to journalArticle

Itenberg, Ilia ; Katzarkov, Ludmil ; Mikhalkin, Grigory ; Zharkov, Ilia. / Tropical Homology. In: Mathematische Annalen. 2018 ; pp. 1-44.
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