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Complete intersections in affine algebraic varieties and Stein spaces

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1092)

Keywords

  • Vector Bundle
  • Complete Intersection
  • Noetherian Ring
  • Holomorphic Vector Bundle
  • Ideal Sheaf

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References

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. C. Banica, O. Forster: Complete intersections in Stein manifolds. Manuscr. Math. 37 (1982) 343–356.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. H. Bass: Algebraic K-theory. Benjamin 1968.

    Google Scholar 

  4. M. Boratyński: A note on set theoretic complete intersections. J. of Algebra 54 (1978) 1–5.

    CrossRef  MATH  Google Scholar 

  5. R.C. Cowsik, M.V. Nori: Curves in characteristic p are set theoretic complete intersections. Inv. Math. 45 (1978) 111–114.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. D. Eisenbud, E.G. Evans: Three conjectures about modules over polynomial rings. Conf. on Commutative Algebra. Springer Lecture Notes in Math. 311 (1973) 78–89.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. D. Eisenbud, E.G. Evans: Every algebraic set in n-space is the intersection of n hypersurfaces. Inv. Math. 19 (1973) 278–305.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. D. Ferrand: Courbes gauches et fibrés de rang deux. C.R. Acad. Sci. Paris 281 (1975) 345–347.

    MathSciNet  MATH  Google Scholar 

  9. O. Forster: Über die Anzahl der Erzeugenden eines Ideals in einem Noetherschen Ring. Math. Zeits. 84 (1964) 80–87.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. O. Forster: Zur Theorie der Steinschen Algebren und Moduln. Math. Zeits. 97 (1967) 376–405.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. O. Forster: Lectures on Riemann surfaces. Springer 1981.

    Google Scholar 

  12. O. Forster, K.J. Ramspott: Über die Darstellung analytischer Mengen. Sb. Bayer. Akad. Wiss., Math.-Nat. Kl., Jg. 1963, 89–99.

    Google Scholar 

  13. O. Forster, K.J. Ramspott: Okasche Paare von Garben nichtabelscher Gruppen. Inv. Math. 1 (1966) 260–286.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. O. Forster, K.J. Ramspott: Analytische Modulgarben und Endromisbündel, Inv. Math. 2 (1966) 145–170.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. B. Giesecke: Simpliziale Zerlegung abzählbarer analytischer Räume. Math. Zeits. 83 (1964) 177–213.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. H. Grauert: Charakterisierung der holomorph-vollständigen Räume. Mth. Ann. 129 (1955) 233–259.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. H. Grauert: Analytische Faserunden über holomorph-vollständigen Räumen. Math. Ann. 135 (1958) 263–273.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. H. Grauert, R. Remmert: Theory of Stein spaces. Springer 1979.

    Google Scholar 

  19. H. Hamm: Zum Homotopietyp Steinscher Räume. Journal f.d.r.u.a. Math. (Crelle) 338 (1983) 121–135.

    MathSciNet  MATH  Google Scholar 

  20. D. Husemoller: Fibre bundles. 2nd ed. Springer 1975.

    Google Scholar 

  21. M. Kneser: Über die Darstellung algebraischer Raumkurven als Durchschnitte von Flächen. Arch. Math. 11 (1960) 157–158.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. E. Kunz: Einführung in die kommutative Algebra und algebraische Geometrie. Vieweg 1979.

    Google Scholar 

  23. S. Łojasiewicz: Triangulation of semi-analytic sets. Ann. Scuola Sup. Pisa (3) 18 (1964) 449–474.

    MathSciNet  MATH  Google Scholar 

  24. K. Lønsted: Vector bundles over finite CW-complexes are algebraic. Proc. AMS 38 (1973) 27–31.

    MathSciNet  MATH  Google Scholar 

  25. N. Mohan Kumar: Complete intersections. J. Kyoto Univ. 17 (1977) 533–538.

    MathSciNet  MATH  Google Scholar 

  26. N. Mohan Kumar: On two conjectures about polynomial rings. Inv. Math. 46 (1978) 225–236.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. P. Murthy: Affine varieties as complete intersections. Int. Symp. Algebraic Geometry Kyoto (1977) 231–236.

    Google Scholar 

  28. D. Quillen: Projective modules over polynomial rings. Inv. Math. 36 (1976) 167–171.

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. A. Sathaye: On the Forster-Eisenbud-Evans conjecture. Inv. Math. 46 (1978) 211–224.

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. M. Schneider: Vollständige, fast-vollständige und mengentheoretisch vollständige Durchschnitte in Steinschen Mannigfaltigkeiten. Math. Ann. 260 (1982) 151–174.

    CrossRef  MathSciNet  MATH  Google Scholar 

  31. M. Schneider: On the number of equations needed to describe a variety. Conference on Several Complex Variables, Madison 1982. To appear in Proc. Symp. Pure Math. AMS 1983.

    Google Scholar 

  32. N. Steenrod: The topology of fibre bundles. Princeton Univ. Press 1951.

    Google Scholar 

  33. U. Storch: Bemerkung zu einem Satz von M. Kneser. Arch. Math. 23 (1972) 403–404.

    CrossRef  MathSciNet  MATH  Google Scholar 

  34. A.A. Suslin: Projective modules over a polynomial ring are free (Russian). Dokl. Acad. Nauk SSSR 229 (1976) 1063–1066.

    MathSciNet  MATH  Google Scholar 

  35. A.A. Suslin: On stably free modules (Russian). Mat. Sbornik 102 (1977) 537–550.

    MathSciNet  MATH  Google Scholar 

  36. R.G. Swan: The number of generators of a module. Math. Zeits. 102 (1967) 318–322.

    CrossRef  MathSciNet  MATH  Google Scholar 

  37. L. Szpiro: Lectures on equations defining a space curve. Tata Inst. of Fund. Research, Bombay. Springer 1979.

    Google Scholar 

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© 1984 Springer-Verlag

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Forster, O. (1984). Complete intersections in affine algebraic varieties and Stein spaces. In: Greco, S., Strano, R. (eds) Complete Intersections. Lecture Notes in Mathematics, vol 1092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099355

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  • DOI: https://doi.org/10.1007/BFb0099355

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  • Print ISBN: 978-3-540-13884-6

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