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On a theorem of Ax

Author: Shulim Kaliman
Journal: Proc. Amer. Math. Soc. 133 (2005), 975-977
MSC (2000): Primary 14E25, 14R10
Published electronically: August 4, 2004
MathSciNet review: 2117196
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Abstract | References | Similar Articles | Additional Information

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 $2$, is an automorphism.

References [Enhancements On Off] (What's this?)

  • [A] James Ax, Injective endomorphisms of varieties and schemes, Pacific J. Math. 31 (1969), 1–7. MR 0251036
  • [B] A. Borel, Injective endomorphisms of algebraic varieties, Arch. Math. (Basel) 20 (1969), 531–537. MR 0255545
  • [G] M. Gromov, Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. (JEMS) 1 (1999), no. 2, 109–197. MR 1694588, 10.1007/PL00011162
  • [H] Robin Hartshorne, Algebraic de Rham cohomology, Manuscripta Math. 7 (1972), 125–140. MR 0313255
  • [I] S. Iitaka, On logarithmic Kodaira dimension of algebraic varieties, Complex analysis and algebraic geometry, Iwanami Shoten, Tokyo, 1977, pp. 175–189. MR 0569688
  • [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

Received by editor(s): June 5, 2002
Received by editor(s) in revised form: November 20, 2003
Published electronically: August 4, 2004
Additional Notes: The author was partially supported by NSA grant MDA904-03-1-0009
Communicated by: Michael Stillman
Article copyright: © Copyright 2004 American Mathematical Society