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Archiv der Mathematik

, Volume 85, Issue 6, pp 527–537 | Cite as

Notes on very ample vector bundles on 3-folds

  • Hidetoshi Maeda
  • Andrew J. Sommese
Original Paper

Abstract.

Let \(\mathcal{E}\) be a very ample vector bundle of rank two on a smooth complex projective threefold X. An inequality about the third Segre class of \(\mathcal{E}\) is provided when \(K_{X} + \det \mathcal{E}\) is nef but not big, and when a suitable positive multiple of \(K_{X} + \det \mathcal{E}\) defines a morphism X → B with connected fibers onto a smooth projective curve B, where K X is the canonical bundle of X. As an application, the case where the genus of B is positive and \(\mathcal{E}\) has a global section whose zero locus is a smooth hyperelliptic curve of genus ≧ 2 is investigated, and our previous result is improved for threefolds.

Mathematics Subject Classification (2000).

Primary 14J60 Secondary 14F05 14C20 14J30 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of Mathematical Sciences, School of Science and EngineeringWaseda UniversityTokyoJapan
  2. 2.Department of MathematicsUniversity of Notre DameNotre DameU. S. A

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