no. 3
Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1
[Déformation des applications holomorphes sur des variétés de Fano de second et quatrième nombre de Betti égaux à 1]
Hwang, Jun-Muk1
1 Korea Institute for Advanced Study 207-43 Cheongryangri-dong Seoul, 130-722 (Korea)
Annales de l'Institut Fourier, Tome 57 (2007) no. 3, pp. 815-823.

Soit X une variété de Fano avec b 2 =1 différente de l’espace projectif et telle que tout couple de surfaces dans X ont des classes fondamentales dans H 4 (X,C) proportionnelles. Soit f:Y→X une application surjective d’une variété projective Y dans X. Nous montrons que toute déformation de f de Y dans X (fixés), provient d’automorphismes de X. La preuve est obtenue en étudiant la géométrie des variétés intégrales du feuilletage multi-valué défini par la variété des vecteurs tangents des courbes rationnelles minimales de X.

Let X be a Fano manifold with b 2 =1 different from the projective space such that any two surfaces in X have proportional fundamental classes in H 4 (X,C). Let f:Y→X be a surjective holomorphic map from a projective variety Y. We show that all deformations of f with Y and X fixed, come from automorphisms of X. The proof is obtained by studying the geometry of the integral varieties of the multi-valued foliation defined by the variety of minimal rational tangents of X.

DOI : 10.5802/aif.2278
Classification : 14J45, 32H02
Keywords: minimal rational curves, Fano manifold, deformation of holomorphic maps
Mot clés : courbes rationnelles minimales, variété de Fano, déformation des applications holomorphes

Hwang, Jun-Muk 1

1 Korea Institute for Advanced Study 207-43 Cheongryangri-dong Seoul, 130-722 (Korea) 
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Hwang, Jun-Muk. Deformation of holomorphic maps onto Fano manifolds  of second and fourth Betti numbers 1. Annales de l'Institut Fourier, Tome 57 (2007) no. 3, pp. 815-823. doi : 10.5802/aif.2278. https://aif.centre-mersenne.org/articles/10.5802/aif.2278/

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