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Singular surfaces and the rigidity of ℙ3

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Abstract

In this paper we give two elementary proofs for the rigidity of the complex projective space ℙ3 with respect to global deformations.

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References

  1. Artin, M.: On isolated rational singularities of surfaces Amer. J. Math. 88, 129–136 (1966)

    Google Scholar 

  2. Altmann, A.; Kleiman, S.: Introduction to Grothendieck duality theory. Lecture Notes in Math. 146, Springer Berlin-Heidelberg-New York 1970

    Google Scholar 

  3. Brieskorn, E.: Rationale Singularitäten komplexer Flächen Inv. Math. 4, 336–358 (1968)

    Google Scholar 

  4. Banica, C.; Stanasila, O.: Algebraic methods in the global theory of complex spaces. New York, Wiley 1976

    Google Scholar 

  5. Brenton,; Morrow, J.: Compactifications of ℂn. Trans. Amer. Math. Soc. 246, 139–153 (1978)

    Google Scholar 

  6. Barth, W; Peters, A; van de Ven, V.: Compact complex surfaces. Erg. d. Math. 3. Folge Band 4. Springer 1984

  7. Esnault, H.: Reflexive modules on quotient surface singularities. J.f.d. reine u. angew. Math. 362, 63–71 (1985)

    Google Scholar 

  8. Fischer, G.: Complex Analytic Geometry. Lecture Notes in Math. 538. Springer 1976

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

    Google Scholar 

  10. Hartshorne, R.: Algebraic Geometry. Graduate Texts 49, Springer, 1977

  11. Hirzebruch, F.; Kodaira, K.: On the complex projective spaces. J. Math. Pur. Appl. 36, 201–216 (1957)

    Google Scholar 

  12. Iitaka, S.: Algebraic geometry. Graduate Texts in Math. 76, Springer 1982

  13. Mori, S.: Threefolds whose canonical bundles are not numerically effective. Ann. Math. 116, 133–176 (1982)

    Google Scholar 

  14. Moi¯sezon, B.: On n-dimensional compact varieties with n algebraically independent meromorphic functions. Am. Math. Soc. Transl. 63, 51–177 (1967)

    Google Scholar 

  15. Nakamura, I.: Moisezon 3-folds homeomorphic to ℙ3. J. Math. Soc. Japan, 39, 521–535 (1987)

    Google Scholar 

  16. Peternell, Th.: Algebraic structures on certain 3-folds. Math. Ann. 274, 133–156 (1986)

    Google Scholar 

  17. Peternell, Th.: On the rigidity problem for the complex projective space. Proceedings of the Journées complexes 1985, Ed. D. Barlet. Nancy 1986

  18. Peternell, Th.; Schneider, M.: Compactifications of ℂ3, I. Math. Ann. 280, 129–146 (1988)

    Google Scholar 

  19. Ueno, K.: Classification theory of algebraic varieties and compact complex spaces. Lecture Notes in Math. 439. Springer, Berlin Heidelberg, New York 1975

    Google Scholar 

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  1. Mathematisches Institut, Postfach 10 12 51, 8580, Bayreuth

    Thomas Peternell

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  1. Thomas Peternell
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Peternell, T. Singular surfaces and the rigidity of ℙ3 . Manuscripta Math 63, 69–82 (1989). https://doi.org/10.1007/BF01173702

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