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Remarks on the Nakano Vanishing Theorem

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Contributions to Several Complex Variables

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Abstract

In this note we give a numerical version of k-ampleness for line bundles (Definition 1) and prove a vanishing theorem (Theorem 2) of Nakano type for these bundles. This vanishing theorem yields a Lefschetz-type theorem (Theorem 3). We begin by reviewing the Nakai-Moishezon-Kleiman criterion for ampleness on which our numerical condition is based.

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Author information

Authors and Affiliations

  1. Johns Hopkins University, Baltimore, Maryland, 21218, USA

    Bernard Shiffman

Authors
  1. Bernard Shiffman
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Notre Dame, Post Office Box 398, Notre Dame, Indiana, 46556, USA

    Alan Howard (Professors) & Pit-Mann Wong (Professors) (Professors) &  (Professors)

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© 1986 Springer Fachmedien Wiesbaden

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Shiffman, B. (1986). Remarks on the Nakano Vanishing Theorem. In: Howard, A., Wong, PM. (eds) Contributions to Several Complex Variables. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-06816-7_12

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  • DOI: https://doi.org/10.1007/978-3-663-06816-7_12

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-08964-1

  • Online ISBN: 978-3-663-06816-7

  • eBook Packages: Springer Book Archive

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