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
Arnold, V.Chapitres Supplémentaires de la Théorie des Équations Différentielles Ordinaires, Éditions Mir, Chapitre 5, (1980).
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).
Camacho, C. and Sad, P. Invariant varieties through singularities of vector fields,Annals of Math.,115, 579–595 (1982).
Camacho, C. Dicritical singularities of holomorphic vector fields,Contemporary Mathematics,269, 39–46, (2001).
Grauert, H. Über modifikationen und exzeptionelle analytische Mengen,Math. Annalen.,146, 331–368, (1962).
Gunning, R.Lectures on Riemann Surfaces, Princeton University Press, 1966.
Laufer, H.Normal Two-Dimensional Singularities, Princeton University Press, 1971.
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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