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Topology of families of affine plane curves

100%
Vui H., Son P.
Annales Polonici Mathematici
|
1999
|
tom 71
|
nr 2
129-139
EN
We determine bifurcation sets of families of affine curves and study the topology of such families.
2
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Order functions of plurisubharmonic functions

100%
Ibrahim Celik H., Poletsky E. A.
Studia Mathematica
|
1997
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tom 124
|
nr 2
161-171
EN
We consider the following problem: find on $ℂ^2$ a plurisubharmonic function with a given order function. In particular, we prove that any positive ambiguous function on $ℂℙ^1$ which is constant outside a polar set is the order function of a plurisubharmonic function.
3
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Geometric classes of Goursat flags and the arithmetics of their encoding by small growth vectors

75%
Mormul P.
Open Mathematics
|
2004
|
tom 2
|
nr 5
859-883
EN
Goursat distributions are subbundles, of codimension at least 2, in the tangent bundles to manifolds having the flag of consecutive Lie squares of ranks not depending on a point and growing-very slowly-always by 1. The length of a flag thus equals the corank of the underlying distribution. After the works of, among others, Bryant&Hsu (1993), Jean (1996), and Montgomery&Zhitomirskii (2001), the local behaviours of Goursat flags of any fixed length r≥2 are stratified into geometric classes encoded by words of length r over the alphabet {G,S,T} (Generic, Singular, Tangent) starting with two letters G and having letter(s) T only directly after an S, or directly after another T. It follows from [6] that the Goursat germs sitting in any fixed geometric class have, up to translations by rk D−2, one and the same small growth vector (at the reference point) that can be computed recursively in terms of the G,S,T code. In the present paper we give explicit solutions to the recursive equations of Jean and show how, thanks to a surprisingly neat underlying arithmetics, one can algorithmically read back the relevant geometric class from a given small growth vector. This gives a secondary, Gödel-like super-encoding of the geometric classes of Goursat objects (rather than just a 1-1 correspondence between those classes and small growth vectors).
4
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Generalization of p-regularity notion and tangent cone description in the singular case

75%
Grzegorczyk W., Medak B., Tret’yakov A. A.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
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2012
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tom 66
|
nr 2
EN
The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions.
5
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Remark on the equisingularity of families of affine plane curves

75%
Vui H., Son P. k.
Annales Polonici Mathematici
|
1998
|
tom 68
|
nr 3
275-280
EN
We give some criteria for the equisingularity of families of affine plane curves.
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