1,018 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
On frobenius splitting of orbit closures of spherical subgroups in flag varieties
Let be a connected spherical subgroup of a semisimple algebraic group
. In this paper, we give a criterion for -orbit closures in the flag
variety of to have nice geometric and cohomological properties. Our main
tool is the method of Frobenius splitting and of global F-regularity
Frobenius splitting and geometry of -Schubert varieties
Let be an equivariant embedding of a connected reductive group over
an algebraically closed field of positive characteristic. Let denote a
Borel subgroup of . A -Schubert variety in is a subvariety of the
form \diag(G) \cdot V, where is a -orbit closure in . In
the case where is the wonderful compactification of a group of adjoint
type, the -Schubert varieties are the closures of Lusztig's -stable
pieces. We prove that admits a Frobenius splitting which is compatible with
all -Schubert varieties. Moreover, when is smooth, projective and
toroidal, then any -Schubert variety in admits a stable Frobenius
splitting along an ample divisors. Although this indicates that -Schubert
varieties have nice singularities we present an example of a non-normal
-Schubert variety in the wonderful compactification of a group of type
. Finally we also extend the Frobenius splitting results to the more
general class of -Schubert varieties.Comment: Final version, 44 page
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