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1
Content available The non-Keller mapping with one zero at infinity
Biernat G., Ciekot A.
Journal of Applied Mathematics and Computational Mechanics
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2016
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Vol. 15, nr 4
5--10
EN
In this paper the polynomial mapping of two complex variables having one zero at infinity is considered. Unlike with Keller mapping, if determinant of the Jacobian of this mapping is constant then it must be zero.
2
Content available About some properties of jacobian for polynomial mappings of two complex variables
Gawroński B., Jankowska J., Moltzan R., Włodarczyk I., Biernat G.
Journal of Applied Mathematics and Computational Mechanics
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2013
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Vol. 12, nr 4
41--46
EN
In our article we consider jacobian Jac(f,h) of polynomial mapping f = Xk Yk +…+ f1, h = Xk–1 Yk–1 +…+ h1. We give conditions for coordinate h in which constant jacobian Jac(f,h) = Jac(f1,h1) vanishes.
3
Content available remote Solving polynomial equations
Jelonek Z.
Demonstratio Mathematica
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2012
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Vol. 45, nr 4
797-805
EN
Let k be a field and (…) be a polynomial isomorphism. We give a formula for (…). In particular we show how to solve the equation (…).
4
Content available remote The Łojasiewicz exponent at infinity of a polynomial of two real variables
Jankowski P.
Bulletin of the Polish Academy of Sciences. Mathematics
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2002
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Vol. 50, no 1
25-31
EN
It is shown that the Łojasiewicz exponent at infinity of a positively defined polynomial of two real variables is attained on the set of zeros of a partial derivative of this polynomial. The second result is that the set of the Łojasiewicz exponents at infinity of positively defined polynomials is equal to the set of rational numbers.
5
Content available remote Topological characterization of finite mappings
Jelonek Z.
Bulletin of the Polish Academy of Sciences. Mathematics
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2001
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Vol. 49, no 3
279-283
EN
In the paper [4] Krasiński and Spodzieja proved that if f : X -> Y is a Zariski closed non-constant mapping of affine varieties over C (where dim X [is greater than or equal to] 2), then f is finite. In this paper we generalize this result to the case of arbitrary algebraically closed field.
6
Content available remote Note about the set S[f] for a polynomial mapping f : [C^2 --> C^2]
Jelonek Z.
Bulletin of the Polish Academy of Sciences. Mathematics
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2001
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Vol. 49, no 1
67-72
EN
The aim of this paper is to give a simple method of computing the set S[f] of points at which a generically-finite polynomial mapping f : [C^2 --> C^2] is not proper.
7
Content available remote Injections into affine hypersurfaces
Jelonek Z.
Bulletin of the Polish Academy of Sciences. Mathematics
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2000
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Vol. 48, no 1
63-67
EN
Let X be a smooth affine variety of dimension n > 2. Assume that the group H[sub 1](X,Z) is a torsion group and that [chi](X) = 1. Let Y be a projectively smooth affine hypersurface Y [is a subset of] C[sup n+1] of degree d > 1, which is smooth at infinity. Then there is no injective polynomial mapping f : X --> Y. This contradicts a result of Peretz [5].
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