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Niels Lauritzen; Jesper Funch Thomsen
Maximal compatible splitting and diagonals of Kempf varieties
(Scindage compatible maximal et diagonales des variétés de Kempf)
Annales de l'institut Fourier, 61 no. 6 (2011), p. 2543-2575, doi: 10.5802/aif.2682
Article PDF | Reviews MR 2976320 | Zbl 1251.14037
Class. Math.: 14M15, 13A35
Keywords: Special linear group, Schubert variety, Frobenius splitting, maximal multiplicity, Wahl’s conjecture

Résumé - 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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