论文标题
$ k $ - 奇妙的品种和矩形
$K$-rings of wonderful varieties and matroids
论文作者
论文摘要
我们研究了超平面布置的奇妙品种的$ k $环，并提供了仅取决于基础矩阵的组合演示。我们使用此组合演示文稿来定义任意无环的Matroid的$ K $环。 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).作为一种应用，我们为奇妙品种的任意线包的欧拉特征提供了组合公式。我们为增强的奇妙品种提供了类似的结构和结果，并为Deligne-Mumford-Knudsen Moduli空间具有稳定的理性曲线，并具有明显的点。
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.
