Jet Bundles on Projective Space II
Tempelveien 112, 3475 Sætre i Hurum, Bærum, Norway
- Corresponding Author:
- Maakestad H
Tempelveien 112, 3475 Sætre i Hurum
E-mail: [email protected]
Received date: October 21, 2015; Accepted date: November 24, 2015; Published date: December 01, 2015
Citation: Maakestad H (2015) Jet Bundles on Projective Space II. J Generalized Lie Theory Appl S2:001. doi:10.4172/generalized-theory-applications.S2-001
Copyright: © 2015 Maakestad H. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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, ïÂÂX(d))* where X = ïÂÂ(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 ïÂÂl (ïÂÂ(d)) on projective space ïÂÂ(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 ïÂÂX1 (ïÂÂX (d)) for any d ≥ 1. We study the incidence complex for the line bundle ïÂÂ(d) on the projective line and show it is a resolution of the ideal sheaf of I l (ïÂÂ(d)) - the incidence scheme of ïÂÂ(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.