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Foliations on ℂℙ of degree 2 with degenerate singularities.
- Source :
-
Bulletin of the Brazilian Mathematical Society . Sep2013, Vol. 44 Issue 3, p421-454. 34p. - Publication Year :
- 2013
-
Abstract
- In this paper we construct non-singular, locally-closed, algebraic varieties which are sets of foliations on ℂℙ of degree 2 with a certain degenerate singularity. We obtain the dimension and closure of these varieties. To do that we construct a stratification (based on GIT, see [7]) of the space of foliations with respect to the action by change of coordinates. We prove that the set of unstable foliations has two irreducible components. We have the following corollary: a foliation of degree 2 defined by a pencil of conics is unstable if and only if the pencil is unstable. Finallywe give another proof of the fact that there are only 4 foliations of degree 2 with a unique singular point (see [5]). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16787544
- Volume :
- 44
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Brazilian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 91660163
- Full Text :
- https://doi.org/10.1007/s00574-013-0020-z