English

Homology of tropical varieties

Algebraic Geometry 2010-03-16 v3 Combinatorics

Abstract

Given a closed subvariety of an algebraic torus, the associated tropical variety is a polyhedral fan in the space of 1-parameter subgroups of the torus which describes the behaviour of the subvariety at infinity. We show that the link of the origin has only top rational homology if a genericity condition is satisfied. Our result is obtained using work of Tevelev and Deligne's theory of mixed Hodge structures.

Keywords

Cite

@article{arxiv.0711.1847,
  title  = {Homology of tropical varieties},
  author = {Paul Hacking},
  journal= {arXiv preprint arXiv:0711.1847},
  year   = {2010}
}

Comments

13 pages. v2: added Thm 2.4, v3: introduction expanded, references added, published version