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Intersection theory on linear subvarieties of toric varieties

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Abstract

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 \({{\mathrm{Trop}}}(Z)\).

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  1. Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653, Kaiserslautern, Germany

    Andreas Gross

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  1. Andreas Gross
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Gross, A. Intersection theory on linear subvarieties of toric varieties. Collect. Math. 66, 175–190 (2015). https://doi.org/10.1007/s13348-014-0129-4

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