On jet bundles and generalized Verma modules

Details On jet bundles and generalized Verma modules On jet bundles and generalized Verma modules

2008-12-15

arxiv.org/abs/0812.2751v9

Mathematics

Algebraic Geometry

27 pages

Scientific paper

The aim of this paper is to initiate a study of the jet bundles on the grassmannian $X$ over a field of characteristic zero using higher direct images of $G$-linearized sheaves, Lie theoretic methods, enveloping algebra theoretic methods and generalized Verma modules. We calculate the $P$-module of the dual jet bundle $J^l(L)^*$ and prove it equals the $l$'th piece of the canonical filtration for $H^0(X,L)^*$. We use the results obtained to prove the discriminant of any linear system on any grassmannian is irreducible.

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