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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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 |
|---|---|
| Publication: | COMMUNICATIONS IN CONTEMPORARY MATHEMATICS |
| Publisher: | WORLD SCIENTIFIC PUBL CO PTE LTD |
| 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 |
| 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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