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Fibered neighborhoods of curves in surfaces

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Abstract

The aim of this article is to study fibered neighborhoods of compact holomorphic curves embedded in surfaces. It is shown that when the self-intersection number of the curve is sufficiently negative the fibration is equivalent to the linear one defined in the normal bundle to the curve. The obstructions to equivalence in the general case are described.

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References

  1. Arnold, V.Chapitres Supplémentaires de la Théorie des Équations Différentielles Ordinaires, Éditions Mir, Chapitre 5, (1980).

  2. Arnold, V. Bifurcations of invariant manifolds of differential equations and normal forms in neighborhoods of elliptic curves,Funct. Anal. Appl.,10–4, 249–259, (1977).

    Article  Google Scholar 

  3. Camacho, C. and Sad, P. Invariant varieties through singularities of vector fields,Annals of Math.,115, 579–595 (1982).

    Article  MathSciNet  Google Scholar 

  4. Camacho, C. Dicritical singularities of holomorphic vector fields,Contemporary Mathematics,269, 39–46, (2001).

    MathSciNet  Google Scholar 

  5. Grauert, H. Über modifikationen und exzeptionelle analytische Mengen,Math. Annalen.,146, 331–368, (1962).

    Article  MATH  MathSciNet  Google Scholar 

  6. Gunning, R.Lectures on Riemann Surfaces, Princeton University Press, 1966.

  7. Laufer, H.Normal Two-Dimensional Singularities, Princeton University Press, 1971.

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Correspondence to C. Camacho.

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Camacho, C., Movasati, H. & Sad, P. Fibered neighborhoods of curves in surfaces. J Geom Anal 13, 55–66 (2003). https://doi.org/10.1007/BF02930996

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  • DOI: https://doi.org/10.1007/BF02930996

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