Homology of tropical varieties

Details Homology of tropical varieties Homology of tropical varieties

2007-11-12

arxiv.org/abs/0711.1847v3

Collect. Math. 59 (2008), no. 3, 263-273

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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