Frobenius splitting of cotangent bundles of flag varieties and geometry of nilpotent cones

Details Frobenius splitting of cotangent bundles of flag varieties and geometry of nilpotent cones Frobenius splitting of cotangent bundles of flag varieties and geometry of nilpotent cones

1998-09-08

arxiv.org/abs/math/9809039v1

Invent. math. 136 (1999), 603-621.

Mathematics

Algebraic Geometry

LaTeX (amsart, amsmath, xypic), 14 pages

Scientific paper

We use the G-invariant non-degenerate form on the Steinberg module to Frobenius split the cotangent bundle of a flag variety in good prime characteristics. This was previously only known for the general linear group. Applications are a vanishing theorem for pull back of line bundles to the cotangent bundle (proved for the classical groups and G_2 by Andersen and Jantzen and in characteristic zero by B. Broer (for all groups)), normality and rational singularities for the subregular nilpotent variety and good filtrations of the global sections of pull backs of line bundles to the cotangent bundle, which in turn implies good filtrations of cohomology of induced representations.

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