2026-04-27T21:26:42Zhttps://uvadoc.uva.es/oai/request

oai:uvadoc.uva.es:10324/681872025-03-13T13:47:20Zcom_10324_1129com_10324_931com_10324_894col_10324_1193

Corral Pérez, Nuria Sanz Sánchez, Fernando 2012 Let S be a germ of a holomorphic curve at (C2, 0) with finitely many branches S1, . . . , Sr and let I = (I1, . . . , Ir ) ∈ Cr . We show that there exists a nondicritical holomorphic foliation of logarithmic type at 0 ∈ C2 whose set of separatrices is S and having index Ii along Si in the sense of Lins Neto (Lecture Notes in Math. 1345, 192–232, 1988) if the following (necessary) condition holds: after a reduction of singularities π : M →(C2, 0) of S, the vector I gives rise, by the usual rules of transformation of indices by blowing-ups, to systems of indices along components of the total transform ¯S of S at points of the divisor E = π −1(0) satisfying: (a) at any singular point of ¯S the two indices along the branches of ¯S do not belong to Q≥0 and they are mutually inverse; (b) the sum of the indices along a component D of E for all points in D is equal to the self-intersection of D in M. This construction is used to show the existence of logarithmic models of real analytic foliations which are real generalized curves. Applications to real center-focus foliations are considered. application/pdf https://uvadoc.uva.es/handle/10324/68187 eng Springer Real logarithmic models for real analytic foliations in the plane info:eu-repo/semantics/article TEXT UVaDOC. Repositorio Documental de la Universidad de Valladolid Hispana