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On the Prym map of cyclic coverings

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Abstract

We work out the cases in which the Prym map is dominant and generically finite for étale or totally ramified cyclic coverings.

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References

  1. Barth, W., Hulek, K., Peters, C., van de Ven, A.: Compact Complex Surfaces. Springer Verlag, Berlin (2004)

    Book  Google Scholar 

  2. Bardelli, F., Ciliberto, C., Verra, A.: Curves of minimal genus on a general abelian variety. Comp. Math. 96, 115–147 (1995)

    MathSciNet  MATH  Google Scholar 

  3. Birkenhake, Ch., Lange, H.: Complex Abelian Varieties. Grundlagen der Mathematischen Wissenschaften 302. Springer Verlag, Berlin (2004)

    Chapter  Google Scholar 

  4. Donagi, R., Smith, R.: The stucture of the Prym map. Acta Math. 146, 25–185 (1981)

    Article  MathSciNet  Google Scholar 

  5. Faber, C.: Prym varieties of triple cyclic covers. Math. Zeitschrift 199, 61–97 (1988)

    Article  MathSciNet  Google Scholar 

  6. Green, M., Lazarsfeld, R.: On the projective normality of complete linear series on algebraic curves. Inv. Math. 83, 73–90 (1986)

    Article  MathSciNet  Google Scholar 

  7. Lange, H., Ortega, A.: Prym varieties of cyclic coverings. Geom. Dedicata 150, 391–403 (2011)

    Article  MathSciNet  Google Scholar 

  8. Lange, H., Ortega, A.: The Prym map of degree-7 cyclic coverings. Algebra Number Theory 10, 771–801 (2016)

    Article  MathSciNet  Google Scholar 

  9. Marcucci, V.O., Naranjo, J.C.: Prym varieties of double covers of elliptic curves. Int. Math. Res. Not. 6, 1689–1698 (2014)

    Article  Google Scholar 

  10. Nagara, D.S., Ramanan, S.: Polarizations of type (\(1,\ldots,1,2\)) on abelian varieties. Duke Math. J. 80, 157–194 (1995)

    Article  MathSciNet  Google Scholar 

  11. Shimura, G.: On analytic families of polarized abelian varieties and automorphic functions. Ann. Math. (2) 78, 149–193 (1963)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department Mathematik der Universität Erlangen, Erlangen, Germany

    Herbert Lange

  2. Institut für Mathematik, Humboldt Universität zu Berlin, Berlin, Germany

    Angela Ortega

Authors
  1. Herbert Lange
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  2. Angela Ortega
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Correspondence to Angela Ortega.

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Lange, H., Ortega, A. On the Prym map of cyclic coverings. Arch. Math. 111, 621–631 (2018). https://doi.org/10.1007/s00013-018-1242-5

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  • DOI: https://doi.org/10.1007/s00013-018-1242-5

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