# Holomorphic bijections of algebraic sets

Annales Polonici Mathematici (1997)

- Volume: 66, Issue: 1, page 63-66
- ISSN: 0066-2216

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topSławomir Cynk, and Kamil Rusek. "Holomorphic bijections of algebraic sets." Annales Polonici Mathematici 66.1 (1997): 63-66. <http://eudml.org/doc/270017>.

@article{SławomirCynk1997,

abstract = {We prove that every holomorphic bijection of a quasi-projective algebraic set onto itself is a biholomorphism. This solves the problem posed in [CR].},

author = {Sławomir Cynk, Kamil Rusek},

journal = {Annales Polonici Mathematici},

keywords = {quasi-projective algebraic set; w-holomorphic mapping; holomorphic bijections; quasi-projective algebraic sets; weak holomorphic function; singularities},

language = {eng},

number = {1},

pages = {63-66},

title = {Holomorphic bijections of algebraic sets},

url = {http://eudml.org/doc/270017},

volume = {66},

year = {1997},

}

TY - JOUR

AU - Sławomir Cynk

AU - Kamil Rusek

TI - Holomorphic bijections of algebraic sets

JO - Annales Polonici Mathematici

PY - 1997

VL - 66

IS - 1

SP - 63

EP - 66

AB - We prove that every holomorphic bijection of a quasi-projective algebraic set onto itself is a biholomorphism. This solves the problem posed in [CR].

LA - eng

KW - quasi-projective algebraic set; w-holomorphic mapping; holomorphic bijections; quasi-projective algebraic sets; weak holomorphic function; singularities

UR - http://eudml.org/doc/270017

ER -

## References

top- [B] A. Borel, Injective endomorphisms of algebraic varieties, Arch. Math. (Basel) 20 (1969), 531-537. Zbl0189.21402
- [C] S. Cynk, Primary decomposition of algebraic sheaves, preprint, 1995.
- [CR] S. Cynk and K. Rusek, Injective endomorphisms of algebraic and analytic sets, Ann. Polon. Math. 56 (1991), 29-35. Zbl0761.14005
- [Ł] S. Łojasiewicz, Introduction to Complex Analytic Geometry, Birkhäuser, Basel, 1991. Zbl0747.32001
- [N] K. Nowak, Injective endomorphisms of algebraic varieties, Math. Ann. 299 (1994), 769-778. Zbl0803.14007
- [W] H. Whitney, Complex Analytic Varieties, Addison-Wesley, 1972. Zbl0265.32008

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