On the growth of proper polynomial mappings

Effective Nullstellensatz and geometric degree for zero-dimensional ideals

“…Secondo, some very classical combinatory argument due to Perron [Pe], and which is also a basic tool in the work of Jelonek, Płoski and P. CassouNoguès ( [Je], [CN], [CNPł], [Pł1], [Pł2]). This first approach allows us to deal with three particular situations:…”

Polar quotients and singularities at infinity of polynomials in two complex variables

“…If R 0 (T ) ≡ const then Lemma 2.3 reduces to Lemma 2.1 of [Pł1]. If R 0 (T ) ≡ const then the lemma follows from Lemmas 8.2 and 8.3 of [CK2].…”

“…We use this notion to characterize the critical values at infinity. The proof of our main result is based on the notion of the Łojasiewicz exponent at infinity (see [CK1], [CK2], [CN-H], [H], [Pł1]). Y, Z] be the homogeneous form corresponding to f .…”

Injectivity of real polynomial maps and Łojasiewicz exponents at infinity

“…We refer to [11,12] for the problem of estimating L ∞ (F), when F is a real polynomial map, in terms of the degrees of the components of F. We refer to [6,18] for results on the estimation of L ∞ (F) for a complex polynomial map F : C n → C s in terms of the geometric degree of F and the degrees of the component functions of F.…”