Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1
Annales de l'Institut Fourier, Volume 57 (2007) no. 3, p. 815-823

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:YX 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.

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:YX 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.

Received : 2006-05-03
Accepted : 2006-07-06
DOI : https://doi.org/10.5802/aif.2278
Classification:  14J45,  32H02
Keywords: minimal rational curves, Fano manifold, deformation of holomorphic maps
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {3},
     year = {2007},
     pages = {815-823},
     doi = {10.5802/aif.2278},
     zbl = {1126.32011},
     mrnumber = {2336831},
     language = {en},
     url = {aif.centre-mersenne.org/item/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. https://aif.centre-mersenne.org/item/AIF_2007__57_3_815_0/

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