Homology of tropical varieties

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.

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

References in corpus (3)

• Stable pair, tropical, and log canonical compact moduli of del Pezzo surfaces
• Elimination Theory for Tropical Varieties
• The space of tropically collinear points is shellable

Cited by in corpus (2)

• Monodromy Filtrations and the Topology of Tropical Varieties
• Analytification is the limit of all tropicalizations