Let be a Fano manifold with different from the projective space such that any two surfaces in have proportional fundamental classes in . Let be a surjective holomorphic map from a projective variety . We show that all deformations of with and fixed, come from automorphisms of . 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 .
Soit une variété de Fano avec différente de l’espace projectif et telle que tout couple de surfaces dans ont des classes fondamentales dans proportionnelles. Soit une application surjective d’une variété projective dans . Nous montrons que toute déformation de de dans (fixés), provient d’automorphismes de . 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 .
Keywords: minimal rational curves, Fano manifold, deformation of holomorphic maps
Mot clés : courbes rationnelles minimales, variété de Fano, déformation des applications holomorphes
@article{AIF_2007__57_3_815_0, author = {Hwang, Jun-Muk}, title = {Deformation of holomorphic maps onto {Fano} manifolds of second and fourth {Betti} numbers 1}, journal = {Annales de l'Institut Fourier}, pages = {815--823}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {57}, number = {3}, year = {2007}, doi = {10.5802/aif.2278}, zbl = {1126.32011}, mrnumber = {2336831}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2278/} }
TY - JOUR AU - Hwang, Jun-Muk TI - Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1 JO - Annales de l'Institut Fourier PY - 2007 SP - 815 EP - 823 VL - 57 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2278/ DO - 10.5802/aif.2278 LA - en ID - AIF_2007__57_3_815_0 ER -
%0 Journal Article %A Hwang, Jun-Muk %T Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1 %J Annales de l'Institut Fourier %D 2007 %P 815-823 %V 57 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2278/ %R 10.5802/aif.2278 %G en %F AIF_2007__57_3_815_0
Hwang, Jun-Muk. Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1. Annales de l'Institut Fourier, Volume 57 (2007) no. 3, pp. 815-823. doi : 10.5802/aif.2278. http://www.numdam.org/articles/10.5802/aif.2278/
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