# Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1

Jun-Muk Hwang^{[1]}

- [1] Korea Institute for Advanced Study 207-43 Cheongryangri-dong Seoul, 130-722 (Korea)

Annales de l’institut Fourier (2007)

- Volume: 57, Issue: 3, page 815-823
- ISSN: 0373-0956

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topHwang, Jun-Muk. "Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1." Annales de l’institut Fourier 57.3 (2007): 815-823. <http://eudml.org/doc/10243>.

@article{Hwang2007,

abstract = {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 $H_4(X, \mathbf\{C\})$. Let $f:Y\rightarrow X$ 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 $X$.},

affiliation = {Korea Institute for Advanced Study 207-43 Cheongryangri-dong Seoul, 130-722 (Korea)},

author = {Hwang, Jun-Muk},

journal = {Annales de l’institut Fourier},

keywords = {minimal rational curves; Fano manifold; deformation of holomorphic maps; deformations of holomorphic maps},

language = {eng},

number = {3},

pages = {815-823},

publisher = {Association des Annales de l’institut Fourier},

title = {Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1},

url = {http://eudml.org/doc/10243},

volume = {57},

year = {2007},

}

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

PB - Association des Annales de l’institut Fourier

VL - 57

IS - 3

SP - 815

EP - 823

AB - 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 $H_4(X, \mathbf{C})$. Let $f:Y\rightarrow X$ 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 $X$.

LA - eng

KW - minimal rational curves; Fano manifold; deformation of holomorphic maps; deformations of holomorphic maps

UR - http://eudml.org/doc/10243

ER -

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