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On Higher Rank Globally Generated Vector Bundles over a Smooth Quadric Threefold

Part of: (Co)homology theory Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  10 June 2015

E. Ballico ,
S. Huh  and
F. Malaspina
E. Ballico
Affiliation:
Università di Trento, 38123 Povo, Trentino, Italy, (edoardo.ballico@unitn.it)
S. Huh
Affiliation:
Department of Mathematics, Sungkyunkwan University, Cheoncheon-dong, Jangan-gu, Suwon 440-746, Republic of Korea, (sukmoonh@skku.edu)
F. Malaspina
Affiliation:
Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy, (francesco.malaspina@polito.it)
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Abstract

We give a complete classification of globally generated vector bundles of rank 3 on a smooth quadric threefold with c1 ≤ 2 and extend the result to arbitrary higher rank case. We also investigate the existence of globally generated indecomposable vector bundles, and give the sufficient and necessary conditions on numeric data of vector bundles for indecomposability.

Keywords

higher rank vector bundlesglobally generatedsmooth quadric threefold

MSC classification

Primary: 14F99: None of the above, but in this section
Secondary: 14J99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 2 , May 2016 , pp. 311 - 337
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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