alexa Abstract | Jet Bundles on Projective Space II
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article Open Access

Abstract

In previous papers the structure of the jet bundle as P-module has been studied using different techniques. In this paper we use techniques from algebraic groups, sheaf theory, generliazed Verma modules, canonical filtrations of irreducible SL(V)-modules and annihilator ideals of highest weight vectors to study the canonical filtration Ul (g)Ld of the irreducible SL(V)-module H0 (X, X(d))* where X = (m, m + n). We study Ul (g)Ld using results from previous papers on the subject and recover a well known classification of the structure of the jet bundle l ((d)) on projective space (V*) as P-module. As a consequence we prove formulas on the splitting type of the jet bundle on projective space as abstract locally free sheaf. We also classify the P-module of the first order jet bundle X1 (X (d)) for any d ≥ 1. We study the incidence complex for the line bundle (d) on the projective line and show it is a resolution of the ideal sheaf of I l ((d)) - the incidence scheme of (d). The aim of the study is to apply it to the study of syzygies of discriminants of linear systems on projective space and grassmannians.

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Author(s): Maakestad H

Keywords

Algebraic group, Jet bundle, Grassmannian, P-module, Generalized verma module, Higher direct image, Annihilator ideal, Canonical filtration, Discriminant, Koszul complex, Regular sequence, Resolution, Lie Theory, Lie bracket, Lie algebra, Topology, Lie triple systems

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