Maximal compatible splitting and diagonals of Kempf varieties
Algebraic Geometry
2010-08-31 v2 Representation Theory
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.
Keywords
Cite
@article{arxiv.1004.2847,
title = {Maximal compatible splitting and diagonals of Kempf varieties},
author = {Niels Lauritzen and Jesper Funch Thomsen},
journal= {arXiv preprint arXiv:1004.2847},
year = {2010}
}
Comments
Revised according to referee suggestions. To appear in Annales de l'Institut Fourier