A Schwarz lemma for canonical algebraic manifolds

Kwack, Myung H.

doi:10.1090/S0002-9939-1973-0326008-6

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A Schwarz lemma for canonical algebraic manifolds
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by Myung H. Kwack PDF

Proc. Amer. Math. Soc. 41 (1973), 219-222 Request permission

Abstract:

It was proved that a holomorphic mapping with a fixed point between a canonical algebraic manifold is biholomorphic if and only if the absolute value of the determinant of its differential at the fixed point is 1.

References

Phillip A. Griffiths, Holomorphic mapping into canonical algebraic varieties, Ann. of Math. (2) 93 (1971), 439–458. MR 281954, DOI 10.2307/1970883
Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770
H. Wu, Normal families of holomorphic mappings, Acta Math. 119 (1967), 193–233. MR 224869, DOI 10.1007/BF02392083