Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Automorphism groups of spaces of minimal rational curves on Fano manifolds of Picard number $1$


Authors: Jun-Muk Hwang and Ngaiming Mok
Translated by:
Journal: J. Algebraic Geom. 13 (2004), 663-673
DOI: https://doi.org/10.1090/S1056-3911-04-00357-1
Published electronically: February 18, 2004
MathSciNet review: 2072766
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Abstract | References | Additional Information

Abstract: Let $X$ be a Fano manifold of Picard number $1$ and $M$ an irreducible component of the space of minimal rational curves on $X$. It is a natural problem to understand the extent to which the geometry of $X$ is captured by the geometry of $M$. In this vein we raise the question as to whether the canonical map $\operatorname{Aut}_o(X) \to \operatorname{Aut}_o(M)$ is an isomorphism. After providing a number of examples showing that this may fail in general, we show that the map is indeed an isomorphism under the additional assumption that the subvariety of $M$ consisting of members passing through a general point $x \in X$is irreducible and of dimension $\geq 2$.


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Additional Information

Jun-Muk Hwang
Affiliation: Department of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Seoul 130-012, Korea
Email: jmhwang@ns.kias.re.kr

Ngaiming Mok
Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Email: nmok@hkucc.hku.hk

DOI: https://doi.org/10.1090/S1056-3911-04-00357-1
Received by editor(s): April 9, 2002
Published electronically: February 18, 2004
Additional Notes: The first author was supported by Grant No. 98-0701-01-5-L from the KOSEF. The second author was supported by a CERG of the Research Grants Council of Hong Kong

American Mathematical Society