# Linear holonomy groups of algebraic solutions of polynomial differential equations

Annales de l'institut Fourier (1997)

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

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topSad, 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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- [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
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- [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] 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] J. MUCIÑO, Deformations of Holomorphic Foliations having a Meromorphic First Integral, J. Reine Angew. Math., 461 (1995). Zbl0816.32022MR96e:32026
- [9] Y. SIU, Techniques of Extension of Analytic Objects, M. Dekker, 1974. Zbl0294.32007MR50 #13600

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