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On complex projective surfaces with trigonal hyperplane sections

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An Erratum to this article was published on 01 December 1990

Abstract

Let S be a complex projective surface endowed with an ample and spanned line bundle L. Assume that (S,L) does not belong to some special classes and that cl(L)2≥10. We prove that(KS⊗L)·KS≤−3 and |L| contains a trigonal curve (of genus≥4) iff either (S,L) is a rational surface ruled by cubics, or the g1 3 of C is cut out by |KS ⊗−1|. This result applies to surface having a hyperplane section which is a trigonal curve.

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Authors and Affiliations

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

    Sonia Brivio & Antonio Lanteri

Authors
  1. Sonia Brivio
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  2. Antonio Lanteri
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Partially supported by the M.P.I. of the Italian Government

An erratum to this article is available at http://dx.doi.org/10.1007/BF02568492.

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Brivio, S., Lanteri, A. On complex projective surfaces with trigonal hyperplane sections. Manuscripta Math 65, 83–92 (1989). https://doi.org/10.1007/BF01168368

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  • DOI: https://doi.org/10.1007/BF01168368

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