대한수학회지 (Journal of the Korean Mathematical Society)

  • 제40권4호
  • /
  • Pages.595-607
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  • 2003
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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SOME EXAMPLES OF HYPERBOLIC HYPERSURFACES IN THE COMPLEX PROJECTIVE SPACE

  • 발행 : 2003.07.01
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초록

In the previous paper [6], the author constructed hyperbolic hypersurfaces of degree $2^{n}$ in the n-dimensional complex projective space for every $n\;\geq\;3$. The purpose of this paper is to give some improvement of this result and to show some general methods of constructions of hyperbolic hypersurfaces of higher degree, which enable us to construct hyperbolic hypersurfaces of degree d in the n-dimensional complex projective space for every $d\;\geq\;2\;{\times}\;6^{n}$.

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참고문헌

  1. Trans. Amer. Math. Soc. v.235 Compact manifolds and hyperbolicity R.Brody https://doi.org/10.2307/1998216
  2. Duke Math. J. v.44 A family of smooth hyperbolic hypersurfaces in P₃ R.Brody;M.Green https://doi.org/10.1215/S0012-7094-77-04440-4
  3. Proc. Sympos. Pure Math. v.62 Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials J.P.Demailly
  4. Amer. J. Math. v.122 Hyperbolicity of generic surfaces of high degree in projective 3-space J.P.Demaily;J.El Goul https://doi.org/10.1353/ajm.2000.0019
  5. Aspect of Math. v.E21 Value distribution theory of the Gauss map of minimal surfaces in $R^m$ H.Fujimoto
  6. Complex Variables v.43 A family of hyperbolic hypersurfaces in the complex projective space H.Fujimoto https://doi.org/10.1080/17476930108815318
  7. Manuscripta Math. v.90 Algebraic families of smooth hyperbolic surfaces of low degree in P³c J.El Goul https://doi.org/10.1007/BF02568323
  8. Marcel Dekker Hyperbolic manifolds and holomorphic mappings S.Kobayashi
  9. Math. Ann. v.304 A construction of hyperbolic hypersurface of Pⁿ(C) K.Masuda;J.Noguchi https://doi.org/10.1007/BF01446298
  10. Duke. Math. J. v.58 Hyperbolic surfaces in P³ A.Nadel https://doi.org/10.1215/S0012-7094-89-05835-3
  11. Proc. Amer. Math. Soc. v.130 Hyperbolic hypersurfaces in Pⁿ(C) of Fermat-Waring type B.Shiffman;M.Zaidenberg
  12. Kodai Math. J. v.23 A hyperbolic hypersurface of degree 10 M.Shirosaki https://doi.org/10.2996/kmj/1138044265
  13. Amer. J. Math v.119 Defects for ample divisors of abelian vaarieties, Schwarz lemma, and hyperbolic hypersurfaces of low degrees Y.T.Siu;S.K.Yeung https://doi.org/10.1353/ajm.1997.0033