Return to Colloquia & Seminar listing
K-rings of wonderful varieties and matroids
Algebraic Geometry and Number Theory| Speaker: | Sam Payne, UT Austin |
| Location: | |
| Start time: | Wed, Apr 19 2023, 4:10PM |
Joint work with Matt Larson, Shiyue Li, and Nick Proudfoot. We show that the K-ring of the wonderful compactification of the complement of a hyperplane arrangement has a combinatorial presentation that depends only on the underlying matroid. This allows us to define and study the K-ring of an arbitrary loopless matroid. We show, in particular, that the K-ring of a loopless matroid is related to the Chow ring of the matroid by an exceptional Hirzebruch-Riemann-Roch isomorphism with integer coefficients, generalizing a result of Berget-Eur-Spink-Tseng for the Boolean matroid. As an application, we give closed formulas for Euler characteristics of line bundles on wonderful compactifications.