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K-rings of wonderful varieties and matroids
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K-rings of wonderful varieties and matroids
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We study the $K$-ring of the wonderful variety of a hyperplane arrangement and give a combinatorial presentation that depends only on the underlying matroid. We use this combinatorial presentation to define the $K$-ring of an arbitrary loopless matroid. We construct an exceptional isomorphism, with integer coefficients, to the Chow ring of the matroid that satisfies a Hirzebruch--Riemann--Roch-type formula, generalizing a recent construction of Berget, Eur, Spink, and Tseng for the permutohedral variety (the wonderful variety of a Boolean arrangement). As an application, we give combinatorial formulas for Euler characteristics of arbitrary line bundles on wonderful varieties. We give analogous constructions and results for augmented wonderful varieties, and for Deligne--Mumford--Knudsen moduli spaces of stable rational curves with marked points.
Forward citations
Cited by 2 Pith papers
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Tangent classes of matroids and wonderful compactifications
Danus constructs an integral matroid tangent class in K_Z(M,G) that matches wonderful-model tangents, recovers Chow Hilbert series via HRR, and obeys Chern-alpha bounds, reproducing Cheng's concurrent work.
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Tangent classes of matroids and wonderful compactifications
An integral tangent class is constructed in the combinatorial K-ring of every loopless matroid with a Feichtner–Yuzvinsky building set, reproducing the tangent class and its key properties from [Che26].
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