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pro vyhledávání: '"PLOSKI, ARKADIUSZ"'
Given an algebroid plane curve $f=0$ over an algebraically closed field of characteristic $p\geq 0$ we consider the Milnor number $\mu(f)$, the delta invariant $\delta(f)$ and the number $r(f)$ of its irreducible components. Put $\bar \mu(f)=2\delta(
Externí odkaz:
http://arxiv.org/abs/2207.14523
We investigate properties of the contact exponent (in the sense of Hironaka [Hi]) of plane algebroid curve singularities over algebraically closed fields of arbitrary characteristic. We prove that the contact exponent is an equisingularity invariant
Externí odkaz:
http://arxiv.org/abs/1910.00320
Publikováno v:
Singularities, Algebraic Geometry, Commutative Algebra and Related Topics. Festschrift for Antonio Campillo on the Occasion of his 65th Birthday. G.M. Greuel, L. Narva\'ez and S. Xamb\'o-Descamps eds. Springer, (2018), 119-133
The Milnor formula $\mu=2\delta-r+1$ relates the Milnor number $\mu$, the double point number $\delta$ and the number $r$ of branches of a plane curve singularity. It holds over the fields of characteristic zero. Melle and Wall based on a result by D
Externí odkaz:
http://arxiv.org/abs/1812.06512
Publikováno v:
Colloquium Mathematicum 156 (2019), 243-254
We prove an intersection formula for two plane branches in terms of their semigroups and key polynomials. Then we provide a strong version of Bayer's theorem on the set of intersection numbers of two branches and apply it to the logarithmic distance
Externí odkaz:
http://arxiv.org/abs/1710.05346
Publikováno v:
Bulletin of the London Mathematical Society (2016) 48 (1): 94-98
\noindent Let $\mu(f)$ resp. $c(f)$ be the Milnor number resp. the degree of the conductor of an irreducible power series $f\in \bK[[x,y]]$, where $\bK$ is an algebraically closed field of characteristic $p\geq 0$. It is well-known that $\mu(f)\geq c
Externí odkaz:
http://arxiv.org/abs/1505.07075
Autor:
Ploski, Arkadiusz
We provide the detailed proof of a strengthened version of the M. Artin Approximation Theorem.
Externí odkaz:
http://arxiv.org/abs/1505.04709
Akademický článek
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Publikováno v:
Semigroup Forum (2016) 92(3), 534-540
We characterize in terms of characteristic sequences the semigroups corresponding to branches at infinity of plane affine curves $\Gamma$ for which there exists a polynomial automorphism mapping $\Gamma$ onto the axis $x=0$.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/1407.0514
Publikováno v:
Universitatis Iagellonicae Acta Mathematica, LII (2015), 7-14
Abhyankar and Moh in their fundamental paper on the embeddings of the line in the plane proved an important inequality which can be stated in terms of the semigroup associated with the branch at infinity of a plane algebraic curve. In this note we st
Externí odkaz:
http://arxiv.org/abs/1407.0176
Autor:
Płoski, Arkadiusz
Let $f=0$ be a plane algebraic curve of degree $d>1$ with an isolated singular point at the origin of the complex plane. We show that the Milnor number $\mu_0(f)$ is less than or equal to $(d-1)^2-\left[\frac{d}{2}\right]$, unless $f=0$ is a set of $
Externí odkaz:
http://arxiv.org/abs/1305.5102