GET THE APP

..

Journal of Generalized Lie Theory and Applications

ISSN: 1736-4337

Open Access

Jet Bundles on Projective Space II

Abstract

Maakestad H

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, ï��X(d))* where X = ï��(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 ï��l (ï��(d)) on projective space ï��(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 ï��X1 (ï��X (d)) for any d ≥ 1. We study the incidence complex for the line bundle ï��(d) on the projective line and show it is a resolution of the ideal sheaf of I l (ï��(d)) - the incidence scheme of ï��(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.

PDF

Share this article

50+ Million Readerbase

Journal Highlights

Google Scholar citation report
Citations: 1926

Journal of Generalized Lie Theory and Applications received 1926 citations as per Google Scholar report

Journal of Generalized Lie Theory and Applications peer review process verified at publons

Indexed In

 
arrow_upward arrow_upward