Jet bundles on projective space II

Details Jet bundles on projective space II Jet bundles on projective space II

2010-03-03

arxiv.org/abs/1003.0816v1

Mathematics

Algebraic Geometry

Scientific paper

Let G=SL(E) be the special linear algebraic group on E where E is a finite dimensional vector space over a field K of characteristic zero. In this paper we study the canonical filtration of the dual G-module of global sections of a G-linearized invertible sheaf L on the grassmannian G/P where P in G is the parabolic subgroup stabilizing a subspace W in E. We classify the canonical filtration as P-module and as a consequence we recover known formulas on the P-module structure of the jet bundle J(L) on projective space. We study the incidence complex for the invertible sheaf O(d) on the projective line and prove it gives a resolution of the incidence scheme I(O(d)) of O(d). The aim of this study is to apply it to the study of resolutions of ideal sheaves of discriminants of invertible sheaves on grassmannians and flag varieties. We also give an elementary proof of the Cauchy formula.

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