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arXiv · 1004.2847

Maximal compatible splitting and diagonals of Kempf varieties

Niels Lauritzen·Jesper Funch Thomsen
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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.

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Niels Lauritzen, Jesper Funch Thomsen. 2010-08-30. Maximal compatible splitting and diagonals of Kempf varieties. https://arxiv.org/abs/1004.2847

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