Poincare problem for divisors invariant by one-dimensional foliations on smooth algebraic variety
| dc.creator | Correa, Mauricio | |
| dc.date | 2009-01-07 | |
| dc.date | 2009-01-24 | |
| dc.date.accessioned | 2026-07-07T12:33:33Z | |
| dc.date.available | 2026-07-07T12:33:33Z | |
| dc.description | In this paper we consider the question of bounding the degree of an divisor $D$ invariant by a $\F$ holomorphic foliation, without rational first integral, on smooth algebraic variety $X$ in terms of degree of $\F$ and some invariants of $D$ and $X$. Particularly, if $\F$ is a foliation of degree $d$ on $\mathbb{P}_{\mathbb{C}}^2$, whose the number of invariants curves is greater that ${k+2\choose k}$, we show that there exist a number $\mathcal{M}(d,k)$ such that if $k>\mathcal{M}(d,k),$ then $\F$ admits a rational first integral of degree $\leq k$. Moreover, there exist a number $\mathscr{G}(d,k)$, such that if $\F$ has an algebraic solution of degree $k$ and genus smaller than $\mathscr{G}(d,k)$, then it has a rational first integral of degree $\leq k$. | |
| dc.identifier | https://arxiv.org/abs/0901.0745 | |
| dc.identifier | http://arxiv.org/abs/0901.0745 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217164 | |
| dc.subject | Geometric Topology | |
| dc.subject | Dynamical Systems | |
| dc.title | Poincare problem for divisors invariant by one-dimensional foliations on smooth algebraic variety | |
| dc.type | text |