Linear holonomy groups of algebraic solutions of polynomial differential equations

Paulo Sad

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 1, page 123-138
  • ISSN: 0373-0956

Abstract

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We consider the problem of realization of a linear subgroup of C * as the linear holonomy group of an algebraic curve which is a leaf of a foliation of CP ( 2 ) .

How to cite

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Sad, Paulo. "Linear holonomy groups of algebraic solutions of polynomial differential equations." Annales de l'institut Fourier 47.1 (1997): 123-138. <http://eudml.org/doc/75223>.

@article{Sad1997,
abstract = {We consider the problem of realization of a linear subgroup of $\{\bf C\}^*$ as the linear holonomy group of an algebraic curve which is a leaf of a foliation of $\{\bf CP\}(2)$.},
author = {Sad, Paulo},
journal = {Annales de l'institut Fourier},
keywords = {foliations in the plane projective space; algebraic leaf; holonomy group; degree of a foliation; theorem of Riemann–Roch; Cousin problem},
language = {eng},
number = {1},
pages = {123-138},
publisher = {Association des Annales de l'Institut Fourier},
title = {Linear holonomy groups of algebraic solutions of polynomial differential equations},
url = {http://eudml.org/doc/75223},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Sad, Paulo
TI - Linear holonomy groups of algebraic solutions of polynomial differential equations
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 1
SP - 123
EP - 138
AB - We consider the problem of realization of a linear subgroup of ${\bf C}^*$ as the linear holonomy group of an algebraic curve which is a leaf of a foliation of ${\bf CP}(2)$.
LA - eng
KW - foliations in the plane projective space; algebraic leaf; holonomy group; degree of a foliation; theorem of Riemann–Roch; Cousin problem
UR - http://eudml.org/doc/75223
ER -

References

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  1. [1] C. CAMACHO and P. SAD, Invariant Varieties through Singularities of Holomorphic Vector Fields, Ann. of Math., 115 (1982). Zbl0503.32007MR83m:58062
  2. [2] H. CARTAN, Sur les Fonctions de Deux Variables Complexes, Bull. des Sci. Math., 54 (1930). Zbl56.0981.04JFM56.0981.04
  3. [3] X. GÓMEZ-MONT and J. MUCIÑO, Persistent Cycles for Holomorphic Foliations Having a Meromorphic First Integral, Lect. Notes in Math., 1345, Springer-Verlag (1988). Zbl0681.58032MR90b:58220
  4. [4] H. GRAUERT and R. REMMERT, Theory of Stein Spaces, Springer-Verlag, 1977. Zbl0379.32001
  5. [5] R. GUNNING, Lectures on Riemann Surfaces, Princeton Univ. Press, 1966. Zbl0175.36801MR34 #7789
  6. [6] Y. ILYASHENKO, The Origin of Limit Cycles under Pertubation of the Equation dw/dz = Rz/Rw, where R(z, w) is a Polynomial, Math. USSR Sbornik, 7 (1969). Zbl0194.40102
  7. [7] A. LINS NETO, Complex Codimension One Foliations Leaving a Compact Submanifold Invariant, in Dynamical Systems and Bifurcation Theory, Pitman Research Notes in Math. Series, 160 (1987). Zbl0647.57017MR88m:57036
  8. [8] J. MUCIÑO, Deformations of Holomorphic Foliations having a Meromorphic First Integral, J. Reine Angew. Math., 461 (1995). Zbl0816.32022MR96e:32026
  9. [9] Y. SIU, Techniques of Extension of Analytic Objects, M. Dekker, 1974. Zbl0294.32007MR50 #13600

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