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arXiv · 0711.1847

Homology of tropical varieties

Paul Hacking
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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.

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Paul Hacking. 2008-08-28. Homology of tropical varieties. https://arxiv.org/abs/0711.1847

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