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Hyperelliptic curves in abelian varieties

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References

  1. C.-L. Chai, “Every ordinary sympletic isogeny class in positive characteristic is dense in the moduli,”Invent. Math.,121, 439–479 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  2. G. Cornell and J. Silverman,Arithmetic Geometry, Springer-Verlag (1986).

  3. P. Deligne et al., “Hodge cycles, motives, and Shimura varieties,” In:Lect. Notes Math., Vol. 900, Springer-Verlag (1982).

  4. P. Deligne and D. Mumford, “The irreducibility of the space of curves of given genus,” In:Vol. déd. au Prof. Oscar Zariski, Vol. 36, Publ. IHES (1969), pp. 75–109.

  5. G. van der Geer and M. van der Vlugt, “On the existence of supersingular curves of given genus,”J. Reine Angew. Math.,458, 53–61 (1995).

    MathSciNet  Google Scholar 

  6. A. Grothendieck, “Techniques de descente et théorèmes d'existence en géométrie algébrique, IV. Les schémas de Hilbert,” In:Sém. Bourbaki, Vol. 13 (1960/61).

  7. T. Ibukiyama, T. Katsura, and F. Oort, “Supersingular curves of genus two and class numbers,”Compos. Math.,57, 127–152 (1986).

    MathSciNet  Google Scholar 

  8. S. Lang,Abelian Varieties, Interscience Publ. (1959).

  9. H. W. Lenstra Jr. and F. Oort, “Simple abelian varieties having a prescribed formal isogeny type,”J. Pure Appl. Algebra,4, 47–53 (1974).

    Article  MathSciNet  Google Scholar 

  10. K.-Z. Li and F. Oort,Moduli of supersingular abelian varieties, Utrecht University preprint 824, Sept. 1993.

  11. Yu. I. Manin, “The theory of commutative formal groups over fields of finite characteristic,”Usp. Mat. Nauk,18, 3–90 (1963);Russ. Math. Surveys,18, 1–80 (1963).

    MATH  MathSciNet  Google Scholar 

  12. L. Moret-Bailly, “Familles de courbes et de variétés abéliennes sur ℙ1,”Astérisque,86, 109–140 (1981).

    MATH  Google Scholar 

  13. S. Mori, “Projective manifolds with ample tangent bundle,”Ann. Math.,110, 593–606 (1979).

    MATH  Google Scholar 

  14. P. Norman and F. Oort, “Moduli of abelian varieties,”Ann. Math.,112, 413–439 (1980).

    MathSciNet  Google Scholar 

  15. F. Oort, “Subvarieties of moduli schemes,”Invent. Math.,24, 95–119 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  16. F. Oort, “Hyperelliptic supersingular curves,” In:Arithmetic Algebraic Geometry, Texel Conference, 1989 (G. van der Geer, F. Oort, J. Steenbrink, eds.), Progr. Math. 89, Birkhäuser (1991), pp. 247–284.

  17. F. Oort, “Rational curves in fibers,” to appear.

  18. G. P. Pirola, “Curves on Kummer varieties,”Duke Math. J.,59, 701–708 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  19. G. P. Pirola, “Abel-Jacobi invariant and curves on generic abelian varieties,” In:Abelian Varieties. Proc. Internat. Confer., Egloffstein, October 1993 (W. Barth, K. Hulek, and H. Lange, eds.), De Gruyter (1995), pp. 237–249.

  20. C. Schoen, “Bounds for rational points on twists of constant hyperelliptic curves,”J. Reine Angew. Math.,411, 196–204 (1990).

    MATH  MathSciNet  Google Scholar 

  21. Gang Xiao, “Irregularity of surfaces with a linear pencil,”Duke Math. J.,55, 597–602 (1987).

    Article  MATH  MathSciNet  Google Scholar 

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Authors
  1. F. Oort
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  2. J. de Jong
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 34, Algebraic Geometry-5, 1996.

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Oort, F., de Jong, J. Hyperelliptic curves in abelian varieties. J Math Sci 82, 3211–3219 (1996). https://doi.org/10.1007/BF02362468

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