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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 8, Issue 2 (Jan 2008)

Issues

Ample vector bundles with zero loci of small Δ-genera

Antonio Lanteri
  • Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via C. Saldini, 50, 20133 Milano, Italy. Email: lanteri@mat.unimi.it
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Carla Novelli
  • Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via C. Saldini, 50, 20133 Milano, Italy. Email: novelli@mat.unimi.it
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2008-05-21 | DOI: https://doi.org/10.1515/ADVGEOM.2008.016

Abstract

Let X be a smooth complex projective variety endowed with an ample vector bundle ε admitting a global section whose zero locus is a smooth subvariety Z of the expected dimension, and let H be an ample line bundle on X, whose restriction HZ to Z is very ample. Triplets (X, ε, H) are studied and classified under the assumption that the delta genus of (Z, HZ ) is either small (≤ 3) or small in comparison with the corank of ε or the degree.

Key words.: Ample vector bundles; special varieties; Δ-genus; adjunction theory; Fano manifolds

About the article

Received: 2006-12-18

Published Online: 2008-05-21

Published in Print: 2008-04-01


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/ADVGEOM.2008.016.

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[1]
Antonio Lanteri and Carla Novelli
Journal of Algebra, 2010, Volume 323, Number 3, Page 671

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