Zobrazeno 1 - 10
of 26
pro vyhledávání: '"32S65, 32M25"'
Let $\mathcal{F}$ be a holomorphic foliation at $p\in \mathbb{C}^2$, and $B$ be a separatrix of $\mathcal{F}$. Under certain conditions on the reduction of singularities of $\mathcal{F}$ and $B$, we prove the Dimca-Greuel type inequality $\frac{\mu_p
Externí odkaz:
http://arxiv.org/abs/2403.18654
Autor:
Gehlawat, Sahil
Let $\mathcal{F}$ be a Riemann surface foliation on $M \setminus E$, where $M$ is a complex manifold and $E \subset M$ is a closed set. Assume that $\mathcal{F}$ is hyperbolic, i.e., all leaves of the foliation $\mathcal{F}$ are hyperbolic Riemann su
Externí odkaz:
http://arxiv.org/abs/2306.12204
Autor:
Genzmer, Yohann
Abstract. In this article, we provide an algorithm to compute the number of moduli of a germ of curve which is an union of germs of smooth curves in the complex plane.
Comment: 18 pages, 5 figures
Comment: 18 pages, 5 figures
Externí odkaz:
http://arxiv.org/abs/2106.13623
In this paper we study holomorphic foliations on $\mathbb{P}^2$ with only one singular point. If the singularity has algebraic multiplicity one, we prove that the foliation has no invariant algebraic curve. We also present several examples of such fo
Externí odkaz:
http://arxiv.org/abs/2103.00537
Autor:
Bedrouni, Samir, Marín, David
Let $d\geq2$ be an integer. The set $\mathbf{F}(d)$ of foliations of degree $d$ on the complex projective plane can be identified with a Zariski's open set of a projective space of dimension $d^2+4d+2$ on which $\mathrm{Aut}(\mathbb P^2_{\mathbb C})$
Externí odkaz:
http://arxiv.org/abs/2101.11509
Autor:
Bedrouni, Samir, Marín, David
A holomorphic foliation on $\mathbb P^2_{\mathbb C}$, or a real analytic foliation on $\mathbb{P}^{2}_{\mathbb{R}},$ is said to be convex if its leaves other than straight lines have no inflection points. The classification of the convex foliations o
Externí odkaz:
http://arxiv.org/abs/1909.01615
Autor:
Bedrouni, Samir, Marín, David
We show that up to automorphisms of $\mathbb P^2_{\mathbb C}$ there are $14$ homogeneous convex foliations of degree $5$ on $\mathbb P^2_{\mathbb C}.$ We establish some properties of the Fermat foliation $\mathcal F_{0}^{d}$ of degree $d\geq2$ and of
Externí odkaz:
http://arxiv.org/abs/1901.03174
Autor:
Bedrouni, Samir, Marín, David
We show that up to automorphisms of $\mathbb{P}^2_{\mathbb C}$ there are $5$ homogeneous convex foliations of degree four on $\mathbb{P}^2_{\mathbb C}.$ Using this result, we give a partial answer to a question posed in $2013$ by D. {Mar\'in} and J.
Externí odkaz:
http://arxiv.org/abs/1811.07735
Autor:
Ardila, Jonny Ardila
We study the existence of first integral for holomorphic foliations in different scenarios and under different conditions, for instance germ of foliations given by vector fields and having a formal first integral or infinitely many invariant hypersur
Externí odkaz:
http://arxiv.org/abs/1502.01901
Publikováno v:
Bull. Braz. Math. Soc. (N.S.), 41 (2010), no. 2, 161--198
The set $\mathscr{F}(2;2)$ of quadratic foliations on the complex projective plane can be identified with a \textsc{Zariski}'s open set of a projective space of dimension 14 on which acts $\mathrm{Aut}(\mathbb{P}^2(\mathbb{C})).$ We classify, up to a
Externí odkaz:
http://arxiv.org/abs/0902.0877