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Frobenius splitting and M\"obius inversion

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arxiv 0902.1930 v1 pith:WTVZC4JN submitted 2009-02-11 math.AG

Allen Knutson This is my paper · ORCID
classification math.AG
keywords classcertaincomputedfrobeniusinversionirreducibleobiusvarieties
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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 M\"obius 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).

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Permutahedra, Lusztig varieties, degenerations, and subdivisions

    math.AG 2026-07 accept novelty 7.0 of 10

    Lusztig varieties degenerate equivariantly inside G/B to unions of Richardson varieties, inducing (regular in types ABC) subdivisions of the permutahedron into Bruhat interval polytopes.

  2. Syzygies of polymatroidal ideals

    math.AC 2025-07 conditional novelty 7.0 of 10

    For every polymatroid, the cave polynomial is valuative, its support is a generalized polymatroid, and its coefficients are the Möbius values, settling the Bandari-Bayati-Herzog and Castillo-Cid-Ruiz-Mohammadi-Montano...

  3. Brion atoms for classical types

    math.RT 2025-12 conditional novelty 6.0 of 10

    Type D Brion atoms are described explicitly and uniformly with the other classical types, giving complete indexing sets for Brion's cohomology formula.

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