2008/12/15 by Maakestad, Helge Øystein
#14L30 #14N15 #17B10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.0812.2751
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 Jl(L)^* and prove it equals the l'th piece of the canonical filtration for H0(X,L)^*. We use the results obtained to prove the discriminant of any linear system on any grassmannian is irreducible.