Cotangent bundles of flag varieties

Abstract

The main aim of this chapter is to give a family of Frobenius splittings of the cotangent bundle T*(G/P) of any flag variety G/P due to Kumar-Lauritzen-Thomsen and thus obtain a cohomology vanishing result for T* (G/P) with coefficients in the line bundles obtained by pullback from G/P. This cohomology vanishing result is applied to study the geometry of nilpotent and subregular cones.