RT info:eu-repo/semantics/article
T1 Real logarithmic models for real analytic foliations in the plane
A1 Corral Pérez, Nuria
A1 Sanz Sánchez, Fernando
K1 Singular holomorphic foliation
K1 Logarithmic foliations
K1 Generalized curves
K1 Center-focus plane vector fields
AB Let S be a germ of a holomorphic curve at (C2, 0) with finitely manybranches S1, . . . , Sr and let I = (I1, . . . , Ir ) ∈ Cr . We show that there exists a nondicriticalholomorphic foliation of logarithmic type at 0 ∈ C2 whose set of separatricesis 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 reductionof singularities π : M →(C2, 0) of S, the vector I gives rise, by the usual rules oftransformation of indices by blowing-ups, to systems of indices along components ofthe total transform ¯S of S at points of the divisor E = π−1(0) satisfying: (a) at anysingular point of ¯S the two indices along the branches of ¯S do not belong to Q≥0 andthey are mutually inverse; (b) the sum of the indices along a component D of E forall points in D is equal to the self-intersection of D in M. This construction is usedto show the existence of logarithmic models of real analytic foliations which are realgeneralized curves. Applications to real center-focus foliations are considered.
PB Springer
SN 1139-1138
YR 2012
FD 2012
LK https://uvadoc.uva.es/handle/10324/68187
UL https://uvadoc.uva.es/handle/10324/68187
LA eng
NO Rev Mat Complut (2012) 25:109–124
DS UVaDOC
RD 02-abr-2025