Journal of Differential Geometry

Residues of holomorphic vector fields relative to singular invariant subvarieties

Daniel Lehmann and Tatsuo Suwa

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 42, Number 1 (1995), 165-192.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214457035

Digital Object Identifier
doi:10.4310/jdg/1214457035

Mathematical Reviews number (MathSciNet)
MR1350698

Zentralblatt MATH identifier
0844.32007

Subjects
Primary: 32S65: Singularities of holomorphic vector fields and foliations
Secondary: 32L30 58F18

Citation

Lehmann, Daniel; Suwa, Tatsuo. Residues of holomorphic vector fields relative to singular invariant subvarieties. J. Differential Geom. 42 (1995), no. 1, 165--192. doi:10.4310/jdg/1214457035. https://projecteuclid.org/euclid.jdg/1214457035


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References

  • [1] P. Baum and R. Bott, On the zeroes of holomorphic vector fields, Essays on Topology and related topics (Memoires dedies a Georges de Rham), Springer, Berlin, 1970, 29-47.
  • [2] P. Baum and R. Bott, Singularities of holomorphic foliations, J. Differential. Geometry 7 (1972) 279-342.
  • [3] R. Bott, Lectures on characteristic classes and foliations, Lectures on Algebraic and Differential Topology, Lecture Notes in Math. Vol. 279, Springer, Berlin, 1972, 1-94.
  • [4] R. Bott, A residue formula for holomorphic vector fields, J. Differential. Geometry 1 (1967) 311-330.
  • [5] C. Camacho and P. Sad, Invariant varieties through^ singularities of holomorphic vector fields, Ann. of Math. 115s fy982) 579-595.
  • [6] B. Gmira, One generalisation d7 un thoreme de C.Camacho et P.Sad relatif aux feuilletages holomorphes singuliers, These de jjjeme C yC i j Lille, 1984. See also: Sur les feuilletages holomorphes singuliers de codimension 1, Publ. Mat. 36 (1992) 229-240.
  • [7] F. Kamber and P. Tondeur, Foliated bundles ard characteristic classes, Lecture Notes in Math. Vol. 493, Spring^, Berlin, 1975.
  • [8] D. Lehmann, Residus des sous varietes invariafts d'un feuilletage singulier, Ann. Inst. Fourier (Grenoble)} 4 1 (1991) 211-258.
  • [9] A. Lins Neto, Algebraic solutions of polynomial differential equations and foliations in dimension two, Holomorphic Dynamics, Mexico 1986, Lecture Notes in Math. Vol. 1345, Sppnger, Berlin, 1988, 192-232.
  • [10] A. Lins Neto, Complex codimension one foliations leaving Bitompact submanifold invariant, Dynamical Systems and Bifufcbution Theory, 1985, Pitman Research Notes in Math. Ser. 160^]kongman Sci. Tech., Harlow, New York, 1987, 295-317.
  • [11] M. Soares, A note on algebraic solutions of foliations in dimension 2, Dynamical Systems and Bifurcation TheoryPl990, Pitman Research Notes in Math. Ser. 285, Longman Sci.^feh., Harlow, New York, 1993, 250-254.
  • [12] T. Suwa, Indices of holomorphic vector fields relative to invariant curves on surfaces, to appear in Proc. Amer. M^th.Soc.