5 citations · 10 across the 14 of their papers we have counts for
5 papers · 2 filters
A c-holomorphic effective Nullstellensatz with parameter
Maciej P. Denkowski
We prove a local Nullstellensatz with parameter for a continuous family of c-holomorphic functions with an effective exponent independent of the parameter: the local degree of the…
Multiplicity and the pull-back problem
Maciej P. Denkowski
We discuss a formula of S. Spodzieja and generalize it for the isolated improper Achilles-Tworzewski-Winiarski intersection index. As an application we give a simple proof of a res…
On the complex Łojasiewicz inequality with parameter
Maciej P. Denkowski
We prove a continuity property in the sense of currents of a continuous family of holomorphic functions which allows us to obtain a Łojasiewicz inequality with an effective exponen…
On the growth exponent of c-holomorphic functions with algebraic graphs
Adam Białożyt, Maciej P. Denkowski, Piotr Tworzewski +1
This paper is the first of a series dealing with c-holomorphic functions defined on algebraic sets and having algebraic graphs. These functions may be seen as the complex counterpa…
The complex gradient inequality with parameter
Maciej P. Denkowski
We prove that given a holomorphic family of holomorphic functions with isolated singularities at zero and constant Milnor number, it is possible to obtain the gradient inequality w…