A characterization of proper regular mappings

  title={A characterization of proper regular mappings},
  author={Tadeusz Krasinski and Stanislaw Spodzieja},
  journal={Annales Polonici Mathematici},
Let X, Y be complex ane varieties and f : X! Y a regular mapping. We prove that if dimX 2 and f is closed in the Zariski topology then f is proper in the classical topology. 



The set of points at which a polynomial map is not proper

We describe the set of points over which a dominant polynomial map f = (f1, . . . , fn) : C → C is not a local analytic covering. We show that this set is either empty or it is a uniruled

A set on which the Łojasiewicz exponent at infinity is attained

We show that for a polynomial mapping F = (f_1,...,f_m): C^n \to C^m the Lojasiewicz exponent at infinity of F is attained on the set {z \in C^n : f_1(z)...f_m(z) = 0}

Algebraic Geometry I: Complex Projective Varieties

Let me begin with a little history. In the 20th century, algebraic geometry has gone through at least 3 distinct phases. In the period 1900-1930, largely under the leadership of the 3 Italians,

Algebraische Geometrie : eine Einführung

Diese Einfuhrung in die algebraische Geometrie richtet sich an Studierende mittlere und hohere Semester. Vorausgesetzt werden lediglich die im ersten Studienjahr erworbenen Grundkenntnisse. Ausgehend

Expansion Techniques in Algebraic Geometry

  • Tata Institute of Fundamental Research, Bombay
  • 1977

Krasiński, Exponent of growth of polynomial mappings of C2 into C2, in: Singularities, S. Łojasiewicz (ed.), Banach Center Publ

  • 1988