Multiplicity Spaces of a Foliation on a / ong att integral Projective Curve .
نویسنده
چکیده
Wc compute te global multiplicity of a 1-dimensional foliation along an integral curve iii projective spaces. Wc give a bound in the way of Poincaré problem for complete intersection curves. In te projective plane, this bound give us a bound of te degree of non irreductible integral Curves in function of te degree of the foliation. O. INTRODUCTION Let jr be a foliation by lines in us take bomogeneous coardinates X0, vector fteld D=Z4(X0 X~) a i=0 ax, te complex projective space P,. Let ., X,. There exists an homogeneous deg(A ~)= a, g.c.d. {A~} = 1 sucb that Y is given by any element of dic set of vector fields a ?i0={D+ffRj where R=XX—5---and H=H(X0, .., >4) is an ho¡—o mogeneous polynomial with deg(H) = d —1, [1], [6]. This number d is said 4 to be tite degree of .7, deg(Y) The solutions of the equatíons — xo A form the set of singularities of 5 and we assume that this set xn Sing(.7) C P~ is finite. • Supported by a grant of IBERDROLA. 1991 Mathematics Subject Classiftcation: 57R25, 51N15, 34A20. Editorial Complutense. Madrid, 1993. http://dx.doi.org/10.5209/rev_REMA.1993.v6.n2.17807
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