RT info:eu-repo/semantics/article
T1 Global Invariant Branches of non-degenerate Foliations on Projective Toric Surfaces
A1 Molina Samper, Beatriz
K1 Foliación
K1 Singular foliations
K1 Invariant curves
K1 Newton polygons
K1 Toric surfaces
K1 1201.01 Geometría Algebraica
AB We prove that the isolated invariant branches of a weak toric type generalized curve de fined over a projective toric ambient sur-faces extend to projective algebraic curves. To do it, we pass through the characterization of the weak toric type foliations in terms of "Newton non-degeneracy" conditions, in the classical sense of Kouchnirenko and Oka. Finally, under the strongest hypothesis of being a toric type foliation, we  nd that there is a dichotomy: Either it has rational fi rst integral but does not have isolated invariant branches or it has  finitely many global invariant curves and all of them are extending isolated invariant branches.
PB Moscow Mathematical Journal
SN 1609-4514
YR 2022
FD 2022
LK https://uvadoc.uva.es/handle/10324/70833
UL https://uvadoc.uva.es/handle/10324/70833
LA eng
NO Moscow Mathematical Journal, 2022, vol. 22, n.3, 493--520
DS UVaDOC
RD 22-nov-2024