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arXiv · 1604.01838

Tropical Homology

Ilia Itenberg·Ludmil Katzarkov·Grigory Mikhalkin·Ilia Zharkov
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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.

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Ilia Itenberg, Ludmil Katzarkov, Grigory Mikhalkin, Ilia Zharkov. 2016-04-07. Tropical Homology. https://arxiv.org/abs/1604.01838

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