Foliations on \(\mathbb{CP}^2\) with a unique singular point without invariant algebraic curves

DOI10.1007/s10711-019-00492-8zbMath1445.37034OpenAlexW2982595650MaRDI QIDQ776204

Claudia R. Alcántara, Rubí Pantaleón-Mondragón

Publication date: 30 June 2020

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-019-00492-8

zbMATH Keywords

invariant algebraic curveholomorphic foliationnilpotent singularitysaddle-node singularity

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Singularities of holomorphic vector fields and foliations (32S65) Complex vector fields, holomorphic foliations, (mathbb{C})-actions (32M25) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Related Items (6)

Special foliations on \(\mathbb{CP}^2\) with a unique singular point ⋮ Foliations on \(\mathbb{P}^2\) with only one singular point ⋮ Plane polynomials and Hamiltonian vector fields determined by their singular points ⋮ A family of dicritical foliations with one singularity ⋮ On the GIT-stability of foliations of degree 3 with a unique singular point ⋮ On the classification of foliations of degree three with one singularity

Cites Work

• Unnamed Item
• Classic geometry of certain quadratic foliations
• A stratification of the Hilbert scheme of points in the projective plane
• Algebraic solutions of one-dimensional foliations
• Equations de Pfaff algébriques
• Description de Hilb sup(n) C{X,Y}
• Foliations on \(\mathbb {CP}^2\) of degree \(d\) with a singular point with Milnor number \(d^2+d+1\)
• Minimal sets of foliations on complex projective spaces
• Singularities of vector fields
• The analytic and formal normal form for the nilpotent singularity. The case of generalized saddle-node
• Polarity with respect ot a foliation and Cayley-Bacharach Theorems
• New examples of holomorphic foliations without algebraic leaves
• A plane foliation of degree different from 1 is determined by its singular scheme
• Birational Geometry of Foliations
• Algebraic Families on an Algebraic Surface

This page was built for publication: Foliations on \(\mathbb{CP}^2\) with a unique singular point without invariant algebraic curves