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Projective manifolds of sectional genus three as zero loci of sections of ample vector bundles

Published online by Cambridge University Press:  01 January 2008

ANTONIO LANTERI  and
HIDETOSHI MAEDA
ANTONIO LANTERI
Affiliation:
Dipartimento di Matematica ‘F. Enriques’, Università degli Studi di Milano, Via C. Saldini, 50, I-20133 Milano, Italy. e-mail: [email protected]
HIDETOSHI MAEDA
Affiliation:
Department of Mathematical Sciences, Faculty of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan. e-mail: [email protected]
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Abstract

Let ϵ be an ample vector bundle of rank r ≥ 2 on a smooth complex projective variety X of dimension n such that there exists a global section of ϵ whose zero locus Z is a smooth subvariety of dimension n-r ≥ 2 of X. Let H be an ample line bundle on X such that the restriction HZ of H to Z is very ample. Triplets (X, ϵ, H) with g(Z, HZ) = 3 are classified, where g(Z, HZ) is the sectional genus of (Z, HZ).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 1 , January 2008 , pp. 109 - 118
Copyright
Copyright © Cambridge Philosophical Society 2008

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