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arXiv · 2011.12452

On characterizations of nondicritical generalized curve foliations

Evelia R. García Barroso·Marcelo E. Hernandes·M. Fernando Hernández Iglesias
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Abstract

We characterize nondicrital generalized curve foliations with fixed reduced separatrix. Moreover, we give suficient conditions when a plane analytic curve is its reduced separatrix. For that, we introduce a distinguished expression for a given 1-form, called {\it Weierstrass form}. Then, using Weierstrass forms, we characterize the nondicritical generalized curve foliations: first, for foliations with monomial separatrix using toric resolution; second, for foliations with reduced separatrix, using the $GSV$-index. In this last case the characterization, which is our main result, could be interpreted in function of a polar of the foliation and a polar of its reduced separatrix.

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Evelia R. García Barroso, Marcelo E. Hernandes, M. Fernando Hernández Iglesias. 2020-11-25. On characterizations of nondicritical generalized curve foliations. https://arxiv.org/abs/2011.12452

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