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Introduction to classification theory of algebraic varieties and compact complex spaces

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References

  1. Artin, M. Algebraization of formal moduli, II. Existence of modification, Ann. of Math., 91 (1970), 88–135.

    Article  MathSciNet  MATH  Google Scholar 

  2. Baily, W.L. On the moduli of Jacobian varieties, Ann. of Math., 71 (1960), 303–314.

    Article  MathSciNet  MATH  Google Scholar 

  3. Blanchard, A. Sur les variétés analytiques complexes, Ann. Ecole Norm. Sup., 73 (1956), 157–202.

    MathSciNet  MATH  Google Scholar 

  4. Bombieri, E. Canonical models of surfaces of general type, Publ. Math. IHES., 42 (1973), 171–219.

    Article  MathSciNet  MATH  Google Scholar 

  5. Cartan, H. Quotient of complex analytic spaces. International colloquium on fuction theory, Tata Inst. Bombay (1960), 1–15.

    Google Scholar 

  6. Hironaka, H. Resolution of singularity of an algebraic variety of characteristic zero I, II, Ann. of Math. (1964), 109–326.

    Google Scholar 

  7. —. Bimeromorphic smoothing of a complex — analytic space. Preprint, University of Warwick (1970).

    Google Scholar 

  8. —. Review of S. Kawai’s paper, Math Review, 32, No. 11 (1966), 87–88.

    Google Scholar 

  9. Iitaka, S. Deformations of compact complex surfaces II, J.Math. Soc. Japan, 22 (1970), 247–261.

    Article  MathSciNet  MATH  Google Scholar 

  10. . On D — dimensions of algebraic varieties, J. Math. Soc. Japan, 23 (1971), 356–373.

    Article  MathSciNet  MATH  Google Scholar 

  11. —. Genera and classification of algebraic varieties I (in Japanese), Sugaku, 24 (1972), 14–27.

    MathSciNet  Google Scholar 

  12. Inoue, M. On surfaces of class VII0, to appear in Invent. Math. (see also Proc. Japan Academy, 48 (1972), 445–446).

    Article  Google Scholar 

  13. Kawai, S. On compact complex analytic manifold of complex dimension 3, I, II, J. Math. Soc. Japan, 17 (1965), 438–442, ibid., 21 (1969), 604–616.

    Article  MathSciNet  MATH  Google Scholar 

  14. —. Elliptic fibre spaces over compact surfaces, Comment, Math. Univ. St. Paul, 15 (1967), 119–138.

    MathSciNet  MATH  Google Scholar 

  15. Kobayashi, S. Hyperbolic manifolds and holomorphic mappings. Marcel Dekker, INC., New York (1970).

    MATH  Google Scholar 

  16. Kobayashi, S. and T. Ochiai. Mapping into compact complex manifolds with negative first chern class, J. Math. Soc. Japan, 23 (1971), 137–148.

    Article  MathSciNet  MATH  Google Scholar 

  17. Kodaira, K. On Kähler varieties of restricted type (an intrinsic characterization of algebraic varieties), Ann. of Math., 60 (1954), 28–48.

    Article  MathSciNet  MATH  Google Scholar 

  18. —. On compact analytic surfaces, I, II, III, Ann. of Math., 71 (1960), 111–152, ibid., 77 (1963), 563–626, ibid., 78(1963), 1–40.

    Article  MathSciNet  MATH  Google Scholar 

  19. —. On the structure of compact complex analytic surfaces I, II, III, IV, Amer. J. Math., 86(1964), 751–798, ibid., 88 (1966), 682–721, ibid., 90 (1968), 1048–1066.

    Article  MathSciNet  MATH  Google Scholar 

  20. —. Pluricanonical systems on algebraic surfaces of general type, J. Math. Soc. Japan, 20 (1968), 170–192.

    Article  MathSciNet  MATH  Google Scholar 

  21. Matsushima, Y. On Hodge manifold with zero first chern class, J. Diff. Geometry, 3 (1969), 477–480.

    MathSciNet  MATH  Google Scholar 

  22. Moishezon, B.G. On n — dimensional compact complex manifold with n algebraically independent meromorphic functions I, II, III, Amer, Math. Soc. Translation, 63 (1967), 51–177 (English translation).

    Article  MATH  Google Scholar 

  23. Mumford, D. Geometric invariant theory. Springer Verlag, Berlin, Hiedelberg, New York (1965).

    Book  MATH  Google Scholar 

  24. Nakamura, I. On classification of parallelizable manifolds and small deformations, to appear.

    Google Scholar 

  25. Nakamura, I. and K. Ueno. On addition formula for Kodaira dimensions of analytic fibre bundles whose fibres are Moishezon manifolds, J. Math. Soc. Japan, 25 (1973), 363–391.

    Article  MathSciNet  MATH  Google Scholar 

  26. Popp, H. On moduli of algebraic varieties II, to appear in Compositio Math., 28.

    Google Scholar 

  27. Remmert, R. Meromorphe Funktionen in kompakten komplexen Räumen, Math. Ann., 132 (1956), 277–288.

    Article  MathSciNet  MATH  Google Scholar 

  28. —. Holomorphe und meromorphe Abbildungen komplexer Räume, Math. Ann. 133 (1957), 328–370.

    Article  MathSciNet  MATH  Google Scholar 

  29. Šafarevič, I.R. et al. Algebraic surfaces, Proc. Steklov Inst. Moscow (1965).

    Google Scholar 

  30. Serre, J.P. Géometrie algebrique et géometrie analytique, Ann. Inst. Fourier, 6 (1956), 1–42.

    Article  MATH  Google Scholar 

  31. Ueno, K. On fibre spaces of normally polarized abelian varieties of dimension 2, I, II, III, J. Fac. Sci. Univ. of Tokyo, Sec. IA, 18 (1971), 37–95, ibid., 19 (1972), 163–199, in preparation.

    MathSciNet  MATH  Google Scholar 

  32. —. Classification of algebraic varieties I, II. Compositiv Math., 27 (1973), 277–342, in preparation.

    MathSciNet  MATH  Google Scholar 

  33. —. Classification of algebraic varieties and compact complex spaces. Lecture Note, to appear.

    Google Scholar 

  34. —. On the pluricanonical systems of algebraic manifolds of dimension 3, to appear.

    Google Scholar 

  35. Weil, A. Variétés kählériennes, Hermann, Paris (1958).

    MATH  Google Scholar 

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Herbert Popp

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© 1974 Springer-Verlag

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Ueno, K. (1974). Introduction to classification theory of algebraic varieties and compact complex spaces. In: Popp, H. (eds) Classification of Algebraic Varieties and Compact Complex Manifolds. Lecture Notes in Mathematics, vol 412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066164

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  • DOI: https://doi.org/10.1007/BFb0066164

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  • Print ISBN: 978-3-540-06951-5

  • Online ISBN: 978-3-540-37877-8

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