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Cyclic covers of Pv branched along v + 2 hyperplanes and the generalized Hodge Conjecture for certain abelian varieties

Part of the Lecture Notes in Mathematics book series (LNM,volume 1399)

Keywords

  • Modulus Space
  • Abelian Variety
  • Hodge Structure
  • Primitive Character
  • Invertible Sheaf

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References

  1. Aoki,N.,Some new algebraic cycles on Fermat varieties. preprint

    Google Scholar 

  2. Bloch, S., Algebraic cycles and values of L-functions, Crelles Journal, 350, 94–108 (1984)

    MathSciNet  MATH  Google Scholar 

  3. Bott, R., Tu, L., Differential Forms in Algebraic Topology, Springer, New York (1982)

    CrossRef  MATH  Google Scholar 

  4. Ceresa, G., C is not algebraicly equivalent to C in its Jacobian, Ann. of Math., 117, 285–291 (1983)

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Deligne, P., Hodge cycles on Abelian varieties, Notes by J.S.Milne, in “Hodge cycles, Motives, and Shimura varieties”, Lect. Notes in Math., 900, Springer (1982)

    Google Scholar 

  6. Esnault, H., Fibre de Milnor d'un cone sur une courbe plane singuliere, Invent. Math. 68, 477–496 (1982)

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Fulton, W., Intersection Theory, Springer, New York (1984)

    CrossRef  MATH  Google Scholar 

  8. Gross, B., On the periods of abelian integrals and a formula of Chowla and Selberg, Invent. Math. 45, 193–211 (1978)

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Grothendieck, A., Hodge's general conjecture is false for trivial reasons, Topology 8, 299–303 (1969)

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Harris,B., Homological versus algebraic equivalence in a Jacobian, Proc. Nat. Acad.Sci.USA,Feb. 1983

    Google Scholar 

  11. Hartshorne, R., Algebraic Geometry, Graduate Texts in Mathematics, No. 52, Springer, New York (1977)

    Google Scholar 

  12. Kempf, G., On the geometry of a theorem of Riemann, Ann. of Math. 98, 178–185 (1973)

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Murthy,M.P.,Commutative Algebra II, University of Chicago Lecture Notes in Math. (1976)

    Google Scholar 

  14. Ran, Z., Cycles on Fermat hypersurfaces, Comp. Math. 42, 121–142 (1980)

    MathSciNet  MATH  Google Scholar 

  15. Schoen, C., Hodge classes on self-products of a variety with an automorphism, Comp. Math., 65, 3–32 (1988)

    MathSciNet  MATH  Google Scholar 

  16. Schwarzenberger, R.L.E., Jacobians and symmetric products, Ill. J. Math., 7, 257–268 (1963)

    MathSciNet  MATH  Google Scholar 

  17. Shioda, T., Algebraic cycles on abelian varieites of Fermat type, Math. Ann. 258, 65–80 (1981)

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. Shioda, T., What is known about the Hodge Conjecture?, in Algebraic Varieties and Analytic Varietes, Advanced Studies in Pure Math. 1, 55–68 (1983)

    MathSciNet  Google Scholar 

  19. Shioda, T., The Hodge Conjecture for Fermat Varieties, Math. Ann. 245, 171–199 (1979)

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Steenbrink, J.H.M., Mixed Hodge structures on the vanishing cohomology, in Real and Complex Singularities, Oslo 1976, P.Holm (ed.), Sijthoff and Noordhoff, 525–563 (1977)

    Google Scholar 

  21. Steenbrink, J.H.M., Some remarks about the Hodge Conjecture, report 2 of the mathematical Institute University of Leiden, (1986)

    Google Scholar 

  22. Verdier,J.-L., Le Theoreme de Riemann-Roch pour les varieties algebriques eventuellement singulieres, Sem. Bourbaki 464, Springer Lect. Notes 514 (1975)

    Google Scholar 

  23. Weil, A., Abelian varieties and the Hodge ring, in Collected Papers III, 421–429 (1979)

    Google Scholar 

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© 1989 Springer-Verlag

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Schoen, C. (1989). Cyclic covers of Pv branched along v + 2 hyperplanes and the generalized Hodge Conjecture for certain abelian varieties. In: Barth, WP., Lange, H. (eds) Arithmetic of Complex Manifolds. Lecture Notes in Mathematics, vol 1399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0095974

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  • DOI: https://doi.org/10.1007/BFb0095974

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51729-0

  • Online ISBN: 978-3-540-46791-5

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