Frobenius splitting and Möbius inversion

Abstract

We show that the fundamental class in K-homology of a Frobenius split scheme can be computed as a certain alternating sum over irreducible varieties, with the coefficients computed using Möbius inversion on a certain poset. If G/P is a generalized flag manifold and X is an irreducible subvariety homologous to a multiplicity-free union of Schubert varieties, then using a result of Brion we show how to compute the K_0-class [X] in K_0(G/P) from the Chow class in A_*(G/P).

5 pages

References in corpus (4)

• Positroid varieties I: juggling and geometry
• Matching polytopes, toric geometry, and the non-negative part of the Grassmannian
• Total positivity for cominuscule Grassmannians
• A Combinatorial Approach to Multiplicity-Free Richardson Subvarieties of the Grassmannian

Cited by in corpus (1)

• A Combinatorial Approach to Multiplicity-Free Richardson Subvarieties of the Grassmannian