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Theta divisors of generalized Prym varieties I

Part of the Lecture Notes in Mathematics book series (LNM,volume 1124)

Keywords

  • Theta Function
  • Abelian Variety
  • Divisor Class
  • Effective Divisor
  • Algebraic Subgroup

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. A. Beauville, Variétés de Prym et Jacobiennes intermédiaires, Ann. Sci. Ecole Norm. Sup. 10(1977), 309–391

    MathSciNet  MATH  Google Scholar 

  2. S. Bloch and J.P. Murre, On the Chow group of certain types of Fano threefolds, Compositio Math. 39(1979), 47–105

    MathSciNet  MATH  Google Scholar 

  3. C.H. Clemens and P.A. Griffiths, The intermediate Jacobian of the cubic threefold, Ann. of Math. 95(1972), 281–356

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus, Inst. Hautes Etudes Sci. Publ. Math. 36(1969), 75–109.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. J. Fay, Theta functions on Riemann surfaces Lect. Notes Math. 352, Springer-Verlag, Berlin, 1973.

    MATH  Google Scholar 

  6. P. Griffiths and J. Harris Principles of algebraic geometry J. Wiley & Sons, New York, 1978.

    MATH  Google Scholar 

  7. V. Kanev, Intermediate Jacobians of threefolds with a pencil of Del Pezzo surfaces and generalized Prym varieties, C.R. Acad. Bulgare Sci. 36(1983), 1015–1017

    MathSciNet  MATH  Google Scholar 

  8. A. Krazer, Lehrbuch der Thetafunctionen Teubner 1903.

    Google Scholar 

  9. S. Lang Abelian varieties Interscience tracts in pure and applied mathematics n.7, New York 1959.

    Google Scholar 

  10. J. Lewittes, Riemann surfaces and the theta function, Acta Math. 111(1964), 37–61

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. W. Manger, Die Klassen von topologischen Abbildungen einer geschlossenen Flache auf sich, Math. Z. 44(1939), 541

    CrossRef  MathSciNet  Google Scholar 

  12. D. Markushevich, Numerical invariants of the families of lines on some Fano threefolds, Mat. Sb. 116(1981), 265–288.

    MathSciNet  MATH  Google Scholar 

  13. L. Masiewicki, Universal properties of Prym varieties with an application to algebraic curves of genus five. Trans. Amer. Math. Soc. 222(1976), 221–240.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. P. Puts, On some Fano threefolds that are sections of Grassmanians, Nederl. Akad. Wetensch. Proc. A85(1982), 77–90.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. A. Tikhomirov, The intermediate Jacobian of the double covering of P3 ramified over a quartic, Izv. Akad. Nauk SSSR Ser. Mat. 44(1980), 1329–1377.

    MathSciNet  MATH  Google Scholar 

  16. A.N. Tjurin, Five lectures on three-dimensional varieties, Uspehi Mat. Nauk 29(1972), no. 5, 3–50.

    MathSciNet  Google Scholar 

  17. G. Welters, Abel-Jacobi isogenies for certain types of Fano threefolds, Mathematisch centrum, Amsterdam, 1981

    Google Scholar 

  18. J. Igusa, Theta functions Springer-Verlag, Berlin, 1972.

    CrossRef  MATH  Google Scholar 

  19. D. Mumford, Abelian varieties Lectures in Tata Institute, Bombay, 1968.

    MATH  Google Scholar 

  20. D. Mumford, Prym varieties I, in Contributions to Analysis: A Collection of Papers Dedicated to Lipman Bers, Academic Press, New York, 1974, 325–350.

    Google Scholar 

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© 1985 Springer-Verlag

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Kanev, V. (1985). Theta divisors of generalized Prym varieties I. In: Casas-Alvero, E., Welters, G., Xambó-Descamps, S. (eds) Algebraic Geometry Sitges (Barcelona) 1983. Lecture Notes in Mathematics, vol 1124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075001

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  • DOI: https://doi.org/10.1007/BFb0075001

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15232-3

  • Online ISBN: 978-3-540-39643-7

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