870 research outputs found
Maximal compatible splitting and diagonals of Kempf varieties
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.Comment: Revised according to referee suggestions. To appear in Annales de
l'Institut Fourie
Frobenius splitting of cotangent bundles of flag varieties and geometry of nilpotent cones
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.Comment: LaTeX (amsart, amsmath, xypic), 14 page
Roller chain drive vibration analysis based on a string model with boundaries moving non-smoothly
Roller chain drive analysis: simplified modeling and analysis of the dynamic effects of meshing
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