Geodesic
GEOMETRIC INVARIANT THEORY FOR HOLOMORPHIC FOLIATIONS ON CP2 OF DEGREE 2
Glasgow mathematical journal, Tome 53 (2011) no. 1, pp. 153-168

Voir la notice de l'article provenant de la source Cambridge

DOI

Let 2 be the space of the holomorphic foliations on CP2 of degree 2. In this paper we study the linear action PGL(3, C) × 2 → 2 given by gX = DgX ^(g−1) in the sense of the Geometric Invariant Theory. We obtain a characterisation of unstable and stable foliations according to properties of singular points and existence of invariant lines. We also prove that if X is an unstable foliation of degree 2, then X is transversal with respect to a rational fibration. Finally we prove that the geometric quotient of non-degenerate foliations without invariant lines is the moduli space of polarised del Pezzo surfaces of degree 2.
DOI : 10.1017/S0017089510000674
Mots-clés : Primary 37F75, 14L24 
ALCÁNTARA, CLAUDIA R. GEOMETRIC INVARIANT THEORY FOR HOLOMORPHIC FOLIATIONS ON CP2 OF DEGREE 2. Glasgow mathematical journal, Tome 53 (2011) no. 1, pp. 153-168. doi: 10.1017/S0017089510000674
@article{10_1017_S0017089510000674,
     author = {ALC\'ANTARA, CLAUDIA R.},
     title = {GEOMETRIC {INVARIANT} {THEORY} {FOR} {HOLOMORPHIC} {FOLIATIONS} {ON} {CP2} {OF} {DEGREE} 2},
     journal = {Glasgow mathematical journal},
     pages = {153--168},
     year = {2011},
     volume = {53},
     number = {1},
     doi = {10.1017/S0017089510000674},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000674/}
}
TY  - JOUR
AU  - ALCÁNTARA, CLAUDIA R.
TI  - GEOMETRIC INVARIANT THEORY FOR HOLOMORPHIC FOLIATIONS ON CP2 OF DEGREE 2
JO  - Glasgow mathematical journal
PY  - 2011
SP  - 153
EP  - 168
VL  - 53
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000674/
DO  - 10.1017/S0017089510000674
ID  - 10_1017_S0017089510000674
ER  - 
%0 Journal Article
%A ALCÁNTARA, CLAUDIA R.
%T GEOMETRIC INVARIANT THEORY FOR HOLOMORPHIC FOLIATIONS ON CP2 OF DEGREE 2
%J Glasgow mathematical journal
%D 2011
%P 153-168
%V 53
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000674/
%R 10.1017/S0017089510000674
%F 10_1017_S0017089510000674

Cité par Sources :