Tropical Homology

Ilia Itenberg; Ludmil Katzarkov; Grigory Mikhalkin; Ilia Zharkov

Tropical Homology

Algebraic Geometry 2020-12-09 v3

Authors: Ilia Itenberg , Ludmil Katzarkov , Grigory Mikhalkin , Ilia Zharkov

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.

Keywords

tropical geometry hodge theory cohomology

Cite

@article{arxiv.1604.01838,
  title  = {Tropical Homology},
  author = {Ilia Itenberg and Ludmil Katzarkov and Grigory Mikhalkin and Ilia Zharkov},
  journal= {arXiv preprint arXiv:1604.01838},
  year   = {2020}
}

Comments

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

Tropical Homology

Abstract

Keywords

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