Newton non-degenerate Foliations on Projective Toric Surfaces
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" conditi...
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| Format: | Article |
| Status: | Published version |
| Publication date: | 2022 |
| Country: | España |
| Institution: | Universidad de Valladolid |
| Repository: | UVaDOC. Repositorio Documental de la Universidad de Valladolid |
| OAI Identifier: | oai:uvadoc.uva.es:10324/70833 |
| Online Access: | https://doi.org/10.17323/1609-4514-2022-22-3-493-520 https://uvadoc.uva.es/handle/10324/70833 |
| Access Level: | Open access |
| Keyword: | Foliación Singular foliations Invariant curves Newton polygons Toric surfaces 1201.01 Geometría Algebraica |
| Summary: | 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. |
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