# Injective endomorphisms of algebraic and analytic sets

Annales Polonici Mathematici (1991)

- Volume: 56, Issue: 1, page 29-35
- ISSN: 0066-2216

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topSławomir Cynk, and Kamil Rusek. "Injective endomorphisms of algebraic and analytic sets." Annales Polonici Mathematici 56.1 (1991): 29-35. <http://eudml.org/doc/262495>.

@article{SławomirCynk1991,

abstract = {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.},

author = {Sławomir Cynk, Kamil Rusek},

journal = {Annales Polonici Mathematici},

keywords = {injective endomorphism; Zariski main theorem; polynomial automorphism},

language = {eng},

number = {1},

pages = {29-35},

title = {Injective endomorphisms of algebraic and analytic sets},

url = {http://eudml.org/doc/262495},

volume = {56},

year = {1991},

}

TY - JOUR

AU - Sławomir Cynk

AU - Kamil Rusek

TI - Injective endomorphisms of algebraic and analytic sets

JO - Annales Polonici Mathematici

PY - 1991

VL - 56

IS - 1

SP - 29

EP - 35

AB - 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.

LA - eng

KW - injective endomorphism; Zariski main theorem; polynomial automorphism

UR - http://eudml.org/doc/262495

ER -

## References

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- [6] R. C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall, 1965. Zbl0141.08601
- [7] S. Łojasiewicz, An Introduction to Complex Analytic Geometry, PWN, Warszawa 1988 (in Polish). Zbl0773.32007
- [8] H. Matsumura and P. Monsky, On the automorphisms of hypersurfaces, J. Math. Kyoto Univ. 3 (3) (1964), 347-361. Zbl0141.37401
- [9] J.-P. Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier (Grenoble) 6 (1955-56), 1-42.

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