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On a theorem of Ax
Author(s):
Shulim
Kaliman
Journal:
Proc. Amer. Math. Soc.
133
(2005),
975-977.
MSC (2000):
Primary 14E25, 14R10
Posted:
August 4, 2004
MathSciNet review:
2117196
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Abstract:
We show that in the case of affine and complete algebraic varieties over an algebraically closed field of zero characteristics any endomorphism of such a variety, that is injective on the complement to a subvariety of codimension  , is an automorphism.
References:
-
- [A]
- J. Ax, Injective endomorphisms of varieties and schemes, Pacific J. Math., 31 (1969), 1-7. MR 0251036 (40:4267)
- [B]
- A. Borel, Injective endomorphisms of algebraic varieties, Arch. Math. 20 (1969), 531-537. MR 0255545 (41:206)
- [G]
- M. Gromov, Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. 1:2 (1999), 109-197. MR 1694588 (2000f:14003)
- [H]
- R. Hartshorne, Algebraic De Rham cohomology, Manuscripta Math. 7(1972), 125-140. MR 0313255 (47:1810)
- [I]
- S. Iitaka On logarithmic Kodaira dimension of algebraic varieties, In: Complex Analysis and Algebraic Geometry, 175-189, Kinokuniya, Tokyo, 1977. MR 0569688 (58:27975)
- [OP]
- Open Problems, Workshop on Group Actions on Rational Varieties, edited by G. Freudenburg and P. Russell, CICMA Report 2002-04 (to appear).
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Additional Information:
Shulim
Kaliman
Affiliation:
Department of Mathematics, University of Miami, Coral Gables, Florida 33124
Email:
kaliman@math.miami.edu
DOI:
10.1090/S0002-9939-04-07651-8
PII:
S 0002-9939(04)07651-8
Received by editor(s):
June 5, 2002
Received by editor(s) in revised form:
November 20, 2003
Posted:
August 4, 2004
Additional Notes:
The author was partially supported by NSA grant MDA904-03-1-0009
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2004,
American Mathematical Society
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