Foliations on $\mathbb{CP}^3$ of degree $2$ that have a line as singular set
Abstract
In this work we classify foliations on $\mathbb{CP}^3$ of codimension 1 and degree $2$ that have a line as singular set. To achieve this, we do a complete description of the components. We prove that the boundary of the exceptional component has only 3 foliations up to change of coordinates, and this boundary is contained in a logarithmic component. Finally we construct examples of foliations on $\mathbb{CP}^3$ of codimension 1 and degree $s \geq 3$ that have a line as singular set and such that they form a family with a rational first integral of degree $s+1$ or they are logarithmic foliations where some of them have a minimal rational first integral of degree not bounded.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2022
- DOI:
- 10.48550/arXiv.2212.09845
- arXiv:
- arXiv:2212.09845
- Bibcode:
- 2022arXiv221209845A
- Keywords:
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- Mathematics - Algebraic Geometry;
- 32S65;
- 37F75 (primary);
- 32M25
- E-Print:
- 14 pages. Comments are welcome