COHOMOLOGY GROUPS OF SECTIONS OF HOMOGENEOUS LINE BUNDLES OVER A TOROIDAL GROUP

Cohomology Groups of Deformations of Line Bundles on Complex Tori

The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations of complex tori. Our analysis interpolates between two extreme cases. The first case is a calculation of the space of (cohomological) theta funct...

Structure of Cohomology of Line Bundles on G/B for Semisimple Groups Short running title: Cohomology of Line Bundles

Let G be a connected and simply connected semisimple algebraic group over an algebraically closed field k of characteristic p > 0, T a maximal torus of G and B a Borel subgroup containing T . Each weight in X(T ) determines a line bundle on the flag varietyG/B. It turns out that cohomology of the line bundle is isomorphic to the derived functor of the induction functors from the category of B-m...

Generalised Kostka-foulkes Polynomials and Cohomology of Line Bundles on Homogeneous Vector Bundles

CONTENTS Introduction 1 1. Notation 3 2. Main definitions and first properties 4 3. Cohomology of line bundles and generalised Kostka-Foulkes polynomials 5 4. The little adjoint module and short q-analogues 11 5. Short Hall-Littlewood polynomials 18 6. Miscellaneous remarks 23 References 25 INTRODUCTION Let G be a semisimple algebraic group with Lie algebra g. We consider generalisations of Lus...

Socle Series of Cohomology Groups of Line Bundles on G/B Short running title: Socle Series of Cohomology Groups

The G-module structure of the cohomology groups of line bundles over the flag variety G/B for a semisimple algebraic group G is studied. It is proved that, generically, their socle filtrations satisfy the same sum formula as Andersen’s filtrations if Lusztig’s conjecture is true. Another purpose of this paper is to calculate the socle series of the H0’s for the p-regular weights close to a cham...

Groups of Complex Line Bundles Over Compact Kähler Varieties.