The complement of a generic hypersurface of degree 2n in \(CP^ n\) is not hyperbolic. (English) Zbl 0633.32023

Translation from Sib. Mat. Zh. 28, No.3(163), 91-100 (Russian) (1987; Zbl 0625.32021).


32Q45 Hyperbolic and Kobayashi hyperbolic manifolds
32H25 Picard-type theorems and generalizations for several complex variables
14C20 Divisors, linear systems, invertible sheaves


Zbl 0625.32021
Full Text: DOI


[1] Sh. Kobayashi, ?Hyperbolic manifolds and holomorphic mappings,? Matematika,17, No. 1, 47-96 (1973).
[2] Sh. Kobayashi, ?Intrinsic distances, measures, and geometric function theory,? Bull. Am. Math. Soc.,82, No. 3, 357-416 (1976). · Zbl 0346.32031
[3] M. G. Zaidenberg, ?On theorems of Brody and Green on conditions for complete hyperbolicity of complex manifolds,? Funkts. Anal. Prilozhen.,14, No. 4, 77-78 (1980).
[4] M. G. Zaidenberg, ?Picard’s theorem and hyperbolicity,? Sib. Mat. Zh.,24, No. 6, 44-55 (1983).
[5] M. G. Zaidenberg, ?On the hyperbolic embeddability of complements of divisors and the limiting behavior of the Kobayashi-Royden metric,? Mat. Sb.,127, No. 1, 55-71 (1984).
[6] V. E. Snurnitsyn, ?The complement of 2n hyperplanes inCP n is not hyperbolic,? Mat. Zametki,40, No. 6 (1986). · Zbl 0622.51019
[7] P. Kiernan, ?Hyperbolic submanifolds of complex projective space,? Proc. Am. Math. Soc.,22, No. 3, 603-606 (1968). · Zbl 0182.11101
[8] S. Kleiman, ?Numerical singularity theory,? Usp. Mat. Nauk,35, No. 6, 69-148 (1980). · Zbl 0451.14020
[9] W. Fulton, St. Kleiman, and R. MacPherson, ?About the enumeration of contacts,? in: Algebraic Geometry-Open Problems, Proc. Ravello Conf., May 31?June 5, 1982; Lect. Notes in Math., Vol. 977, Springer-Verlag, Berlin (1983), pp. 156-196.
[10] I. Vainsencher, ?Counting divisors with prescribed singularities,? Trans. Am. Math. Soc.,667, No. 2, 399-422 (1981). · Zbl 0475.14047
[11] V. S. Kulikov, ?Calculus of singularities of the embedding of a generic algebraic surface in the projective space P3,? Funkts. Anal. Prilozhen.,17, No. 3, 15-27 (1983).
[12] V. I. Arnol’d, ?Singularities of ray systems,? Usp. Mat. Nauk,38, No. 2, 77-148 (1983).
[13] E. E. Landis, ?Tangential singularities,? Funkts. Anal. Prilozhen.,15, No. 2, 36-49 (1981).
[14] W. Fulton and R. Lazarsfeld, ?Connectivity and its applications in algebraic geometry,? in: Algebraic Geometry, Proceedings, Lect. Notes in Math., Vol. 862, Springer-Verlag, Berlin (1981), pp. 29-92. · Zbl 0484.14005
[15] J. Hansen, ?A connectedness theorem for flagmanifolds and grassmanians,? Am. J. Math.,105, No. 2, 633-639 (1983). · Zbl 0544.14034
[16] D. Mumford, Algebraic Geometry, I: Complex Projective Varieties, Springer-Verlag, Berlin-New York (1976). · Zbl 0356.14002
[17] J. Humphreys, Linear Algebraic Groups, Springer-Verlag, New York (1975). · Zbl 0325.20039
[18] I. R. Shafarevich, Basic Algebraic Geometry [in Russian], Nauka, Moscow (1972). · Zbl 0253.14006
[19] M. L. Green, ?some examples and counterexamples in value distribution theory for several variables,? Compos. Math.,30, No. 3, 317-322 (1975).
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