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

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 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 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 is irreducible and of dimension .

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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