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Geometry of rays-positive manifolds

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Abstract

Let \({\mathcal {M}}\) be a smooth complex projective variety and let \({\mathcal {L}}\) be a line bundle on it. Rays-positive manifolds, namely pairs \({(\mathcal {M},\mathcal {L})}\) such that \({\mathcal {L}}\) is numerically effective and \({\mathcal {L}\cdot R >0 }\) for all extremal rays R on \({\mathcal {M}}\) , are studied. Several illustrative examples and some applications are provided. In particular, projective varieties with crepant singularities and of small degree with respect to the codimension are classified, and the non-negativity of the sectional genus \({g(\mathcal {M},\mathcal {L})}\) is proven, describing as well the pairs with \({g(\mathcal {M},\mathcal {L})=0,1}\) .

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146, Genoa, Italy

    M. C. Beltrametti

  2. Department of Mathematics, University of Bergen, Johannes Bruns gate 12, 5008, Bergen, Norway

    A. L. Knutsen

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

    A. Lanteri

  4. Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy

    C. Novelli

Authors
  1. M. C. Beltrametti
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  2. A. L. Knutsen
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  3. A. Lanteri
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  4. C. Novelli
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Correspondence to M. C. Beltrametti.

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Beltrametti, M.C., Knutsen, A.L., Lanteri, A. et al. Geometry of rays-positive manifolds. Collect. Math. 63, 375–391 (2012). https://doi.org/10.1007/s13348-011-0048-6

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  • DOI: https://doi.org/10.1007/s13348-011-0048-6

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