K-rings of wonderful varieties and matroids

Abstract: Chow rings of wonderful varieties and matroids have played key roles in solving many long-standing open questions in combinatorics and algebraic geometry. We study the K-rings of wonderful varieties associated with realizable matroids, as deformations of the Chow rings. We also compute the Euler characteristic of every line bundle on wonderful varieties, which has an explicit formula given purely combinatorially by the underlying matroid. We then generalize the Euler characteristic to give a new valuative invariant for an arbitrary matroid. As an application, we study the K-ring and compute the Euler characteristic of every line bundle of $\overline{\mathcal{M}}_{0, n}$, the Deligne-Mumford-Knudsen compactification of the moduli space of rational stable curves of $n$ distinct marked points. Joint work with Matt Larson, Sam Payne and Nicholas Proudfoot.

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