Intersection Theory on Linear Subvarieties of Toric Varieties

Abstract

We give a complete description of the cohomology ring $A^{\ast }(\overline{Z})$ of a compactification of a linear subvariety $Z$ of a torus in a smooth toric variety whose fan $\Sigma$ is supported on the tropicalization of $Z$. It turns out that cocycles on $\overline{Z}$ canonically correspond to Minkowski weights on $\Sigma$ and that the cup product is described by the intersection product on the tropical matroid variety $\mathrm{Trop}(Z)$.

published version

References in corpus (1)

• The diagonal of tropical matroid varieties and cycle intersections

Cited by in corpus (2)

• Intersection Theory on Tropicalizations of Toroidal Embeddings
• Wonderful compactifications and rational curves with cyclic action