Maximal compatible splitting and diagonals of Kempf varieties

2010/04/16 by Lauritzen, Niels, Thomsen, Jesper Funch
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1004.2847

Abstract

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.

Related

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• Algebraic Frobenius Splitting of Cotangent Bundles of Flag Varieties
• Algebraization of Frobenius splitting via quantum groups
• Koszul Property and Frobenius Splitting of Schubert Varieties
• The induced PBW filtration, Frobenius splitting of double flag varieties, and Wahl's conjecture