تقرير
The Poincar\'e problem for reducible curves
| العنوان: | The Poincar\'e problem for reducible curves |
|---|---|
| المؤلفون: | Ayuso, Pedro Fortuny, Ribón, Javier |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Complex Variables, Mathematics - Algebraic Geometry, Mathematics - Classical Analysis and ODEs, Mathematics - Dynamical Systems, 32S05 (Primary), 32S65, 14H20 (Secondary) |
| الوصف: | We provide sharp lower bounds for the multiplicity of a local holomorphic foliation defined in a complex surface in terms of data associated to a germ of invariant curve. Then we apply our methods to invariant curves whose branches are isolated, i.e. they are never contained in non-trivial analytic families of equisingular invariant curves. In this case we show that the multiplicity of an invariant curve is at most twice the multiplicity of the foliation. Finally, we apply the local methods to foliations in the complex projective plane. Comment: 24 pages, 4 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2310.13131 |
| رقم الأكسشن: | edsarx.2310.13131 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |