ScholarLens Back to search
2011•International Journal of MathematicsRequires access

PARABOLIC k-AMPLE BUNDLES

Indranil Biswas, F. Laytimi

Open publisher page 2 citations

Abstract

We construct projectivization of a parabolic vector bundle and a tautological line bundle over it. It is shown that a parabolic vector bundle is ample if and only if the tautological line bundle is ample. This allows us to generalize the notion of a k-ample bundle, introduced by Sommese, to the context of parabolic bundles. A parabolic vector bundle E* is defined to be k-ample if the tautological line bundle [Formula: see text] is k-ample. We establish some properties of parabolic k-ample bundles.

About this research paper

What this paper is about

We construct projectivization of a parabolic vector bundle and a tautological line bundle over it. It is shown that a parabolic vector bundle is ample if and only if the tautological line bundle is ample. This allows us to generalize the notion of a k-ample bundle, introduced by Sommese, to the context of parabolic bundles. A parabolic vector bundle E* is defined to be k-ample if the tautological line bundle [Formula: see text] is k-ample. We establish some properties of parabolic k-ample bundles.

Why it matters

OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We construct projectivization of a parabolic vector bundle and a tautological line bundle over it. It is shown that a parabolic vector bundle is ample if and only if the tautological line bundle is ample. This allows us to generalize the notion of a k-ample bundle, introduced by Sommese, to the context of parabolic bundles. A parabolic vector bundle E* is defined to be k-ample if the tautological line bundle [Formula: see text] is k-ample. We establish some properties of parabolic k-ample bundles.

Key concepts: Vector bundle, Tautological line bundle, Line bundle, Mathematics, Bundle, Frame bundle, Principal bundle, Vector-valued differential form

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
PARABOLIC k-AMPLE BUNDLES — Research Paper | ScholarLens