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EXTENSIONS OF VECTOR BUNDLES WITH APPLICATION TO NOETHER-LEFSCHETZ THEOREMS

Ravindra, GV and Tripathi, Amit (2013) EXTENSIONS OF VECTOR BUNDLES WITH APPLICATION TO NOETHER-LEFSCHETZ THEOREMS. In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 15 (5).

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Official URL: http://dx.doi.org/10.1142/S021919971350003X

Abstract

Given a smooth, projective variety Y over an algebraically closed field of characteristic zero, and a smooth, ample hyperplane section X subset of Y, we study the question of when a bundle E on X, extends to a bundle epsilon on a Zariski open set U subset of Y containing X. The main ingredients used are explicit descriptions of various obstruction classes in the deformation theory of bundles, together with Grothendieck-Lefschetz theory. As a consequence, we prove a Noether-Lefschetz theorem for higher rank bundles, which recovers and unifies the Noether-Lefschetz theorems of Joshi and Ravindra-Srinivas.

Item Type: Journal Article
Additional Information: copyright for this article belongs to WORLD SCIENTIFIC PUBLICATION
Keywords: Vector bundles; algebraic varieties; extensions of bundles; Noether-Lefschetz theorem
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 01 Nov 2013 09:48
Last Modified: 01 Nov 2013 09:48
URI: http://eprints.iisc.ac.in/id/eprint/47672

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