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pro vyhledávání: '"Gwoździewicz, Janusz"'
In this paper we describe the factorization of the higher order polars of a generic branch in its equisingularity class. We generalize the results of Casas-Alvero and Hefez-Hernandes-Hern\'andez to higher order polars.
Externí odkaz:
http://arxiv.org/abs/2410.11732
Autor:
Gryszka, Beata, Gwoździewicz, Janusz
Let $x=t^n$, $y=\sum_{i=1}^{\infty}a_it^i$ be a parametrisation of the germ of a complex plane analytic curve $\Gamma$ at the origin. Then $\Gamma$ has the implicit equation $f(x,y)=0$ in the neighbourhood of the origin, where $f=\sum c_{ij}x^iy^j$ i
Externí odkaz:
http://arxiv.org/abs/2303.11300
Publikováno v:
In Journal of Pure and Applied Algebra September 2024 228(9)
Autor:
Gryszka, Beata, Gwoździewicz, Janusz
Let $\mathbb{K}$ be an uncountable field of characteristic zero and let $f$ be a function from $\mathbb{K}^n$ to $\mathbb{K}$. We show that if the restriction of $f$ to every affine plane $L\subset\mathbb{K}^n$ is regular, then $f$ is a regular funct
Externí odkaz:
http://arxiv.org/abs/2106.08001
Let $(f,g)\colon (\mathbb{C}^2,0)\longrightarrow (\mathbb{C}^2,0)$ be a holomorphic mapping with an isolated zero. We show that the initial Newton polynomial of its discriminant is determined, up to rescalling variables, by the ideals $(f)$ and $(g)$
Externí odkaz:
http://arxiv.org/abs/2104.08567
Autor:
Gwoździewicz, Janusz
We prove that every polynomial map $(f,g):\mathbb{R}^2\to\mathbb{R}^2$ with nowhere vanishing Jacobian such that $\mathrm{deg}\, f\leq 5$, $\mathrm{deg}\,g \leq 6$ is injective.
Externí odkaz:
http://arxiv.org/abs/2003.06193
Akademický článek
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Publikováno v:
International Mathematics Research Notices 2022 (2) (2022), 1045-1080
A quasi-ordinary polynomial is a monic polynomial with coefficients in the power series ring such that its discriminant equals a monomial up to unit. In this paper we study higher derivatives of quasi-ordinary polynomials, also called higher order po
Externí odkaz:
http://arxiv.org/abs/1907.03249
Let $ R $ be a regular local ring with maximal ideal $ \mathfrak{m} $. We consider elements $ f \in R $ such that their Newton polyhedron has a loose edge. We show that if the symbolic restriction of $f$ to such an edge is a product of two coprime po
Externí odkaz:
http://arxiv.org/abs/1904.04194
Autor:
Gwoździewicz, Janusz, Hejmej, Beata
We consider formal power series in several variables with coefficients in arbitrary field such that their Newton polyhedron has a loose edge. We show that if the symbolic restriction of the power series $f$ to such an edge is a product of two coprime
Externí odkaz:
http://arxiv.org/abs/1807.04944