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 University Press

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
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