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# Criteria for Very Ampleness of Rank Two Vector Bundles over Ruled Surfaces

Published:2010-08-18
Printed: Dec 2010
• Alberto Alzati,
Dipartimento di Matematica, Univ. di Milano, 20133 Milano, Italy
• Gian Mario Besana,
College of Computing and Digital Media, De Paul University, Chicago, IL, 60604, U.S.A
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## Abstract

Very ampleness criteria for rank $2$ vector bundles over smooth, ruled surfaces over rational and elliptic curves are given. The criteria are then used to settle open existence questions for some special threefolds of low degree.
 Keywords: vector bundles, very ampleness, ruled surfaces
 MSC Classifications: 14E05 - Rational and birational maps 14J30 - $3$-folds [See also 32Q25]