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Submanifolds of Abelian varieties to Rebecca

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References

  1. Andreotti, A., Frankel, T.: The Lefschetz theorem on hyperplane sections. Ann. of Math.69, 713–717 (1959)

    Article  MathSciNet  Google Scholar 

  2. Barth, W.: Fortsetzung meromorpher Funktionen in Tori und Komplexprojektiven Räumen. Invent. Math.5, 42–62 (1968)

    Article  ADS  MathSciNet  Google Scholar 

  3. Barth, W.: Transplanting cohomology classes in complex-projective space. Amer. J. Math.92, 951–967 (1970)

    Article  MathSciNet  Google Scholar 

  4. Barth, W.: Larsen's theorem on the homotopy group of projective manifolds of small embedding codimension. Proc. Symp. in Pure Math.29, 307–313 (1975)

    Article  MathSciNet  Google Scholar 

  5. Barth, W., Larsen, M.E.: On the homotopy group of complex projective manifolds. Math. Scand.30, 88–94 (1972)

    Article  MathSciNet  Google Scholar 

  6. Bloch, S., Gieseker, D.: The positivity of the Chern classes of an ample vector bundle. Invent. Math.12, 112–117 (1971)

    Article  ADS  MathSciNet  Google Scholar 

  7. Bott, R.: On a theorem of Lefschetz. Mich. Math. J.6, 211–216 (1959)

    Article  Google Scholar 

  8. Grauert, H.: Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann.146, 331–368 (1962)

    Article  MathSciNet  Google Scholar 

  9. Grauert, H., Riemenschneider, O.: Verschwindungssätze für analytisches Kohomologiegruppen auf komplexen Räumen. Invent. Math.11, 263–292 (1970)

    Article  ADS  MathSciNet  Google Scholar 

  10. Griffiths, P.A.: The extension problem in complex analysis. II, (Embeddings with positive normal bundle). Amer. J. Math.88, 366–446 (1966)

    Article  MathSciNet  Google Scholar 

  11. Griffiths, P.A.: Hermitian differential geometry, Chern clesses, and positive vector bundles. In: Global Analysis, Papers in honor of K. Kodaira (185–251). Princeton: Princeton University Press 1969

    Google Scholar 

  12. Hartshorne, R.: Ample vector bundles. Publ. Math. IHES29, 319–350 (1966)

    Article  Google Scholar 

  13. Hartshorne, R.: Ample subvarities of algebraic varieties. Lecture Notes in Mathematics 156. Berlin, Heidelberg, New York: Springer 1970

    Book  Google Scholar 

  14. Hartshorne, R.: Cohomology of non-complete algebraic varieties. Compos. Math.23, 257–264 (1971)

    MathSciNet  Google Scholar 

  15. Hartshorne, R.: Ample vector bundles on curves. Nagoya Math. J.43, 73–89 (1971)

    Article  MathSciNet  Google Scholar 

  16. Hartshorne, R.: Varieties of small codimension in projective space. Bull. Amer. Math. Soc.80, 1017–1032 (1974)

    Article  MathSciNet  Google Scholar 

  17. Hironaka, H.: Smoothing of algebraic cycles of small dimensions. Amer. J. Math.90, 1–54 (1968)

    Article  MathSciNet  Google Scholar 

  18. Hironaka, H.: Bimeromorphic smoothing of a complex-analytic space (Summary). Math. Inst. Warwick University, England, (1971)

    Google Scholar 

  19. Hironaka, H., Matsumura, H.: Formal functions and formal embeddings. J. Math. Soc. Japan20, 52–82 (1968)

    Article  MathSciNet  Google Scholar 

  20. Kleiman, S.L.: Towards a numerical theory of ampleness. Ann. of Math.84, 293–344 (1966)

    Article  MathSciNet  Google Scholar 

  21. Kleiman, S.L.: Ample vector bundles on algebraic surfaces. Proc. Amer. Math. Soc.21, 673–676 (1969)

    Article  MathSciNet  Google Scholar 

  22. Kodaira, K.: On a differential geometric method in the theory of analytic stacks. Proc. Nat. Acad. Sci.38, 1269–1273 (1953)

    MathSciNet  Google Scholar 

  23. Larsen, M.E.: On the topology of complex projective manifolds. Invent. Math.19, 251–260 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  24. Ogus, A.: Local cohomological dimension of algebraic varieties. Ann. of Math.98, 327–365 (1973)

    Article  MathSciNet  Google Scholar 

  25. LePotier, J.: Annulation de la cohomologie à valeurs dans un fibré vectoriel holomorphe positif de rang quelconque. Math. Ann.218, 35–53 (1975)

    Article  MathSciNet  Google Scholar 

  26. LePotier, J.: Cohomologie de la grassmanienne à valeurs dans les puissances exteriures et symétriques du fibre universal. Math. Ann.226, 257–270 (1977)

    Article  MathSciNet  Google Scholar 

  27. Ramanujam, C.P.: Remarks on the Kodaira vanishing theorem. J. Indian Math. Soc.36, 41–50 (1972)

    MathSciNet  Google Scholar 

  28. Riemenschneider, O.: Characterizing Moisezon spaces by almost positive coherent sheaves. Math. Z.123, 263–284 (1971)

    Article  MathSciNet  Google Scholar 

  29. Schneider, M.: Barth-Lefschetz theorems for compact irreducible hermitian symmetric manifolds, talk at Several Complex Variable Conference. Williamstown, Mass. 1975

  30. Schneider, M.: Lefschetzsätze und Hyperkonvexität. Invent. Math.31, 183–192 (1976)

    Article  ADS  Google Scholar 

  31. Schneider, M.: Ein einfacher Beweis des Verschwindungssatzes für positive holomorphe Vektorraumbündel. Manusc. Math.11, 95–101 (1974)

    Article  Google Scholar 

  32. Sommese, A.J.: On manifolds that cannot be ample divisors. Math. Ann.221, 55–72 (1976)

    Article  MathSciNet  Google Scholar 

  33. Sommese, A.J.: Onk-ampleness

  34. Sommese, A.J.: Theorems of Barth-Lefschetz type for complex subspaces of homogeneous complex manifolds. Proc. Nat. Acad. Sci.74, 1332–1333 (1977)

    Article  ADS  MathSciNet  CAS  PubMed  PubMed Central  Google Scholar 

  35. Sommese, A.J.: Concavity theorems

  36. Sommese, A.J.: Complex subspaces of homogeneous complex manifolds, I, II

  37. Speiser, R.D.: Cohomological dimension and abelian varieties. Amer. J. Math.95, 1–34 (1973)

    Article  MathSciNet  Google Scholar 

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  1. Department of Mathematics, Cornell University, White Hall, 14853, Ithaca, NY, USA

    Andrew John Sommese

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Sommese, A.J. Submanifolds of Abelian varieties to Rebecca. Math. Ann. 233, 229–256 (1978). https://doi.org/10.1007/BF01405353

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