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- Title
Equivariant K-Theory Classes of Matrix Orbit Closures.
- Authors
Berget, Andrew; Fink, Alex
- Abstract
The group |$G = \textrm{GL}_r(k) \times (k^\times)^n$| acts on |$\textbf{A}^{r \times n}$| , the space of |$r$| -by- |$n$| matrices: |$\textrm{GL}_r(k)$| acts by row operations and |$(k^\times)^n$| scales columns. A matrix orbit closure is the Zariski closure of a point orbit for this action. We prove that the class of such an orbit closure in |$G$| -equivariant |$K$| -theory of |$\textbf{A}^{r \times n}$| is determined by the matroid of a generic point. We present two formulas for this class. The key to the proof is to show that matrix orbit closures have rational singularities.
- Subjects
ORBITS (Astronomy); K-theory; COLUMNS; MATRICES (Mathematics)
- Publication
IMRN: International Mathematics Research Notices, 2022, Vol 2022, Issue 18, p14105
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnab135