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oai:uvadoc.uva.es:10324/708332025-01-28T07:59:57Zcom_10324_1129com_10324_931com_10324_894col_10324_1193

Molina Samper, Beatriz 2024-10-15T15:21:12Z 2024-10-15T15:21:12Z 2022 Moscow Mathematical Journal, 2022, vol. 22, n.3, 493--520 1609-4514 https://uvadoc.uva.es/handle/10324/70833 10.17323/1609-4514-2022-22-3-493-520 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. eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ Attribution-NonCommercial-NoDerivatives 4.0 Internacional Foliación Newton non-degenerate Foliations on Projective Toric Surfaces info:eu-repo/semantics/article