Frobenius splitting and Möbius inversion

Details Frobenius splitting and Möbius inversion Frobenius splitting and Möbius inversion

2009-02-11

arxiv.org/abs/0902.1930v1

Mathematics

Algebraic Geometry

5 pages

Scientific paper

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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