On a theorem of Ax
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- by Shulim Kaliman PDF
- Proc. Amer. Math. Soc. 133 (2005), 975-977 Request permission
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
- James Ax, Injective endomorphisms of varieties and schemes, Pacific J. Math. 31 (1969), 1–7. MR 251036, DOI 10.2140/pjm.1969.31.1
- A. Borel, Injective endomorphisms of algebraic varieties, Arch. Math. (Basel) 20 (1969), 531–537. MR 255545, DOI 10.1007/BF01899460
- M. Gromov, Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. (JEMS) 1 (1999), no. 2, 109–197. MR 1694588, DOI 10.1007/PL00011162
- Robin Hartshorne, Algebraic de Rham cohomology, Manuscripta Math. 7 (1972), 125–140. MR 313255, DOI 10.1007/BF01679709
- S. Iitaka, On logarithmic Kodaira dimension of algebraic varieties, Complex analysis and algebraic geometry, Iwanami Shoten, Tokyo, 1977, pp. 175–189. MR 0569688
- Open Problems, Workshop on Group Actions on Rational Varieties, edited by G. Freudenburg and P. Russell, CICMA Report 2002-04 (to appear).
Additional Information
- Shulim Kaliman
- Affiliation: Department of Mathematics, University of Miami, Coral Gables, Florida 33124
- MR Author ID: 97125
- Email: kaliman@math.miami.edu
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 975-977
- MSC (2000): Primary 14E25, 14R10
- DOI: https://doi.org/10.1090/S0002-9939-04-07651-8
- MathSciNet review: 2117196