Bounds on leaves of foliations of the plane
| dc.creator | Esteves, E. | |
| dc.creator | Kleiman, S. | |
| dc.date | 2003-04-11 | |
| dc.date.accessioned | 2026-07-07T04:56:47Z | |
| dc.date.available | 2026-07-07T04:56:47Z | |
| dc.description | This paper contributes to the solution of the Poincare problem, which is to bound the degree of a (generalized algebraic) leaf of a (singular algebraic) foliation of the complex projective plane. The first theorem gives a new sort of bound, which involves the Castelnuovo--Mumford regularity of the singular locus of the leaf. The second theorem gives a bound in terms of two singularity numbers of the leaf: the total Tjurina number, and the number of non-quasi-homogeneous singularities. If such singularities are present, then this bound improves one due to du Plessis and Wall, at least when the curve is irreducible. | |
| dc.description | 11 pages; AMSLaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0304147 | |
| dc.identifier | http://arxiv.org/abs/math/0304147 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67050 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37F75 (Primary) 14H50, 32S65, 14H20 (Secondary) | |
| dc.title | Bounds on leaves of foliations of the plane | |
| dc.type | text |