Maximal compatible splitting and diagonals of Kempf varieties

Details Maximal compatible splitting and diagonals of Kempf varieties Maximal compatible splitting and diagonals of Kempf varieties

2010-04-16

arxiv.org/abs/1004.2847v2

Mathematics

Algebraic Geometry

Revised according to referee suggestions. To appear in Annales de l'Institut Fourier

Scientific paper

Lakshmibai, Mehta and Parameswaran (LMP) introduced the notion of maximal multiplicity vanishing in Frobenius splitting. In this paper we define the algebraic analogue of this concept and construct a Frobenius splitting vanishing with maximal multiplicity on the diagonal of the full flag variety. Our splitting induces a diagonal Frobenius splitting of maximal multiplicity for a special class of smooth Schubert varieties first considered by Kempf. Consequences are Frobenius splitting of tangent bundles, of blow-ups along the diagonal in flag varieties along with the LMP and Wahl conjectures in positive characteristic for the special linear group.

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