Tautological classes of matroids

• 成果类型: Article
• 署名作者: Berget, Andrew; Eur, Christopher; Spink, Hunter; Tseng, Dennis
• 署名单位: Western Washington University; Stanford University; Harvard University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01194-5
• 发表日期: 2023
• 页码: 951-1039
• 关键词: k-theory; combinatorial geometries; intersection theory; critical-points; VARIETIES; product; POWERS; ring

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.