Resumen de Intersection theory on linear subvarieties of toric varieties

Andreas Gross

• We give a complete description of the cohomology ring A^*(\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).