X. Gómez-Mont

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In this paper we study foliations F on compact manifolds M , of real codimension 2, with a transversal holomorphic structure. We construct a decomposition of M into dynamically defined components, similar to the Fatou/Julia sets for iteration of rational functions, or the region of discontinuity/limit set partition for Kleinian groups in PSL(2,C). All this(More)
Gómez-Mont, Seade and Verjovsky introduced an index, now called GSV-index, generalizing the Poincaré-Hopf index to complex vector fields tangent to singular hypersurfaces. The GSV-index extends to the real case. This is a survey paper on the joint research with Gómez-Mont and Giraldo about calculating the GSV-index IndV±,0(X) of a real vector field X(More)
Let (V, 0) be a germ of a complete intersection variety in C, n > 0, having an isolated singularity at 0 and X be the germ of a holomorphic vector field on C tangent to V and having on V an isolated zero at 0. We show that in this case the homological index and the GSV-index coincide. In the case when the zero of X is also isolated in the ambient space C we(More)
We introduce the geodesic flow on the leaves of a holomorphic foliation with leaves of dimension 1 and hyperbolic, corresponding to the unique complete metric of curvature -1 compatible with its conformal structure. We do these for the foliations associated to Riccati equations, which are the projectivisation of the solutions of a linear ordinary(More)
Given a commutative square of finite free O-modules, we construct a double complex, that we have called the Gobelin. The Gobelin is weaved with vertical and horizontal strands of the Buchsbaum-Eisenbud type, constructed each from half of the commutative square. We apply the Gobelin to compute the homological index of a germ of a holomorphic vector field on(More)
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