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Publication Date:
19 08 2011
ISSN:
1615-7168
DOI:
10.1515/advgeom.2011.027

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Ample vector bundles and polarized manifolds of sectional genus three

1Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy

2Dipartimento di Matematica “F. Enriques”, Università di Milano, Via C. Saldini 50, 20133 Milano, Italy

Citation Information: Advances in Geometry. Volume 11, Issue 4, Pages 623–636, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: 10.1515/advgeom.2011.027, August 2011

Publication History:

Received: 17/09/2009;
Revised: 04/11/2009;
Published Online: 17/04/2012

Abstract

Let ℰ be an ample vector bundle of rank r ≥ 2 on a smooth complex projective variety X of dimension n having a global section whose zero locus Z is a smooth subvariety of dimension nr ≥ 3 of X. Let H be an ample line bundle on X such that its restriction HZ to Z is generated by global sections. The structure of triplets (X, ℰ, H) is determined under the assumption that (Z, HZ ) has sectional genus g(Z, HZ ) = 3.

Key words.: Ample vector bundles; adjunction theory; polarized varieties; curve genus; special varieties; Fano manifolds

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