Injective endomorphisms of algebraic and analytic sets

• Autorzy: Sławomir Cynk , Kamil Rusek
• Języki publikacji: EN

Abstrakty

EN

We prove that every injective endomorphism of an affine algebraic variety over an algebraically closed field of characteristic zero is an automorphism. We also construct an analytic curve in ℂ⁶ and its holomorphic bijection which is not a biholomorphism.

Kategorie tematyczne

• 32C25: Analytic subsets and submanifolds
• 32C15: Complex spaces
• 14A10: Varieties and morphisms
• 14E99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991-1992
• Tom: 56
• Numer: 1
• Strony: 29-35

Daty

wydano

1991

otrzymano

1989-11-02

poprawiono

1991-03-20

Twórcy

autor

Sławomir Cynk

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

autor

Kamil Rusek

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

• [1] J. Ax, A metamathematical approach to some problems in number theory,, in: Proc. Sympos. Pure Math. 20, Amer. Math. Soc., 1971, 161-190.
• [2] A. Białynicki-Birula and M. Rosenlicht, Injective morphisms of real algebraic varieties, Proc. Amer. Math. Soc. 13 (1962), 200-203.
• [3] A. Borel, Injective endomorphisms of algebraic varieties, preprint.
• [4] J. Dieudonné, Cours de géométrie algébrique, Vol. II, Presses Univ. France, 1974.
• [5] A. Grothendieck, Eléments de géométrie algébrique. IV. Etude locale des schémas et des morphismes de schémas (quatrième partie), Inst. Hautes Etudes Sci. Publ. Math. 32 (1967).
• [6] R. C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall, 1965.
• [7] S. Łojasiewicz, An Introduction to Complex Analytic Geometry, PWN, Warszawa 1988 (in Polish).
• [8] H. Matsumura and P. Monsky, On the automorphisms of hypersurfaces, J. Math. Kyoto Univ. 3 (3) (1964), 347-361.
• [9] J.-P. Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier (Grenoble) 6 (1955-56), 1-42.