Tautological classes of matroids

被引：14

作者：

Berget, Andrew ^{[1
]}

Eur, Christopher ^{[3
]}

Spink, Hunter ^{[2
]}

Tseng, Dennis

机构：

[1] Western Washington Univ, Bellingham, WA 98225 USA

[2] Stanford Univ, Stanford, CA USA

[3] Harvard Univ, Cambridge, MA USA

来源：

INVENTIONES MATHEMATICAE | 2023年 / 233卷 / 02期

基金：

美国国家科学基金会;

关键词：

K-THEORY; COMBINATORIAL GEOMETRIES; INTERSECTION THEORY; CRITICAL-POINTS; VARIETIES; PRODUCT; POWERS; RING;

D O I：

10.1007/s00222-023-01194-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce certain torus-equivariant classes on permutohedral varieties which we call "tautological classes of matroids" as a new geometric framework for studying matroids. Using this framework, we unify and extend many recent developments in matroid theory arising from its interaction with algebraic geometry. We achieve this by establishing a Chow-theoretic description and a log-concavity property for a 4 -variable transformation of the Tutte polynomial, and by establishing an exceptional Hirzebruch-Riemann-Roch-type formula for permutohedral varieties that translates between K-theory and Chow theory.

引用

页码：951 / 1039

页数：89

共 110 条

[1] Hodge theory for combinatorial geometries [J].