Abstract
Let f: Cn⟶C be a weighted homogeneous polynomial with a finite number of critical points. The aim of this paper is to give a formula for the Łojasiewicz exponent of f at infinity in terms of its weights wi, when wi≥2. We also give a characterization of properness for weighted homogeneous polynomial mapppings. As a corollary, we prove the Jacobian conjecture for weighted and preweighted homogeneous polynomial mappings with positive weights.
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