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Attracting divisors on projective algebraic varieties

100%
Stawiska M.
Annales Polonici Mathematici
|
2007
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tom 91
|
nr 2-3
263-270
EN
We obtain sufficient and necessary conditions (in terms of positive singular metrics on an associated line bundle) for a positive divisor D on a projective algebraic variety X to be attracting for a holomorphic map f:X → X.
2
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On regular polynomial endomorphisms of ℂ2 without bounded critical orbitswithout bounded critical orbits

100%
Stawiska M.
Open Mathematics
|
2005
|
tom 3
|
nr 3
398-403
EN
We study conditions involving the critical set of a regular polynomial endomorphism f∶ℂ2↦ℂ2 under which all complete external rays from infinity for f have well defined endpoints.
3
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Liouville theorem with parameters: asymptotics of certain rational integrals in differential fields

100%
Stawiska M.
Commentationes Mathematicae
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2010
|
tom 50
|
nr 2
EN
We study asymptotics of integrals of certain rational functions that depend on parameters in a field K of characteristic zero. We use formal power series to represent the integral and prove certain identities about coefficients of this series following from the generalized Vandermonde determinant expansion. Our result can be viewed as a parametric version of a classical theorem of Liouville. We also give some applications.
4
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Some approximation problems in semi-algebraic geometry

64%
Friedland S., Stawiska M.
Banach Center Publications
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2015
|
tom 107
|
nr 1
133-147
EN
In this paper we deal with a best approximation of a vector with respect to a closed semi-algebraic set C in the space ℝⁿ endowed with a semi-algebraic norm ν. Under additional assumptions on ν we prove semi-algebraicity of the set of points of unique approximation and other sets associated with the distance to C. For C irreducible algebraic we study the critical point correspondence and introduce the ν-distance degree, generalizing the notion developed by other authors for the Euclidean norm. We discuss separately the case of the $ℓ^p$ norm (p > 1).
5
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Lelong classes on toric manifolds and a theorem of Siciak

64%
Branker M., Stawiska M.
Annales Polonici Mathematici
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2012
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tom 106
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nr 1
97-105
EN
We generalize a theorem of Siciak on the polynomial approximation of the Lelong class to the setting of toric manifolds with an ample line bundle. We also characterize Lelong classes by means of a growth condition on toric manifolds with an ample line bundle and construct an example of a nonample line bundle for which Siciak's theorem does not hold.
6
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Weighted pluripotential theory on compact Kähler manifolds

64%
Branker M., Stawiska M.
Annales Polonici Mathematici
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2009
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tom 95
|
nr 2
163-177
EN
We introduce a weighted version of the pluripotential theory on compact Kähler manifolds developed by Guedj and Zeriahi. We give the appropriate definition of a weighted pluricomplex Green function, its basic properties and consider its behavior under holomorphic maps. We also develop a homogeneous version of the weighted theory and establish a generalization of Siciak's H-principle.
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