Journal of Algebraic Geometry

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

Author(s): Jun-Muk Hwang; Ngaiming Mok
Journal: J. Algebraic Geom. 13 (2004), 663-673.
Posted: February 18, 2004
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Abstract: Let

be a Fano manifold of Picard number

and

an irreducible component of the space of minimal rational curves on

. It is a natural problem to understand the extent to which the geometry of

is captured by the geometry of

. 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

consisting of members passing through a general point $x \in X$ is irreducible and of dimension $\geq 2$ .

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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

PII: S 1056-3911(04)00357-1
Received by editor(s): April 9, 2002
Posted: 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

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