4 papers
The gradient of a polynomial at infinity
Jacek Chadzynski, Tadeusz Krasinski
The paper gives a full description of the growth of the gradient of a polynomial in two complex variables at infinity near any fiber of the polynomial
The join of algebraic curves
T. Krasinski
Let X,Y be algebraic curves in P^n over C. We give an effective description of the join J(X,Y)\in P^n of X and Y in terms of local parametrizations of X and Y.
A set on which the local Lojasiewicz exponent is attained
J. Chadzynski, T. Krasinski
Let U be a neighbourhood of 0 \in C^n.We show that for a holomorphic mapping F = (f_1,...,f_m) : U -> C^m, F(0) = 0, the Lojasiewicz exponent of F at 0 is attained on the set {z \i…
A set on which the Lojasieewicz exponent at infinity is attained
J. Chadzynski, T. Krasinski
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}