On some characterization of proper polynomial mappings

• Autorzy: Rodak T. , Spodzieja S.
• Języki publikacji: EN

Abstrakty

EN

It is well known that a proper, in the classical topology, polynomial mapping is closed in the Zariski topology. In the paper we prove that the inverse is true. Namely, any non-constant polynomial mapping from [C^n] into [C^m] which is closed in the Zariski topology is proper in the classical topology.

Słowa kluczowe

EN

finite mapping; Laurent polynomial mapping; Łojasiewicz exponent; polynomial mapping; proper mapping

PL

odwzorowanie skończone; odwzorowanie wielomianowe; odwzorowanie wielomianowe Laurenta; odwzorowanie właściwe; wykładnik Łojasiewicza

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2000
• Tom: Vol. 48, no 2
• Strony: 157--164
• Opis fizyczny: Bibliogr. 5 poz.,

Twórcy

autor

Rodak T.

• Faculty of Mathematics, Łódź University, S. Banacha 22, Pl 90-238 Łódź, Poland

autor

Spodzieja S.

• Faculty of Mathematics, Łódź University, S. Banacha 22, Pl 90-238 Łódź, Poland

Bibliografia

• [1] J. Chądzyński, T. Krasiński, A set on which the Łojasiewicz exponent at infinity is attained, Ann. Polon. Math., 67 (1997) 191-197.
• [2] Z. Jelonek, The set of points at which a polynomial map is not proper, Ann. Polon. Math., 58 (1993) 259-266.
• [3] S. Łojasiewic z, Introduction to complex analytic geometry, Birkhäuser, Basel, Boston, Berlin 1991.
• [4] D. Mumford, Algebraic geometry I, Complex projective varieties, Springer-Verlag, Berlin, Heidelberg, New York 1976.
• [5] P. Tworzewski, T. Winiarski, Analytic sets with proper projection, J. Reine Angew. Math., 337 (1982) 68-76.