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

Journal of Generalized Lie Theory and Applications
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Research Article

Jet Bundles on Projective Space II

Maakestad H*

Tempelveien 112, 3475 Sætre i Hurum, Bærum, Norway

Corresponding Author:
Maakestad H
Tempelveien 112, 3475 Sætre i Hurum
Bærum, Norway
Tel: +4798457343
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.

 

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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