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Projective surfaces with bi-elliptic hyperplane sections

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Abstract

We study projective surfaces X which have a bi-elliptic curve (i.e. 2∶1 covering of an elliptic curve) among their hyperplane sections . We give a complete characterization of those surfaces when their degree d is d≥17 (only conic bundles and scrolls if d≥19, three possible exception otherwise) and when d≤8. A conjecture is given for the remaining cases. The main tool we use is the study of the adjunction mapping on X.

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Authors and Affiliations

  1. Facolta' di Scienze, Universita' di Urbino, Urbino, Italy

    Andrea Del Centina

  2. Dip. di Matematica, Universita' di Genova, Via L. B. Alberti 4, Genova, Italy

    Alessandro Gimigliano

Authors
  1. Andrea Del Centina
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  2. Alessandro Gimigliano
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Del Centina, A., Gimigliano, A. Projective surfaces with bi-elliptic hyperplane sections. Manuscripta Math 71, 253–282 (1991). https://doi.org/10.1007/BF02568405

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