Apéry basis and polar invariants of plane curve singularities
type: Item
instance of: scholarly article
title: Apéry basis and polar invariants of plane curve singularities
zbMATH Open document ID: 0728.14029
published in: Pacific Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Let C be an irreducible plane algebroid curve singularity defined by \(f\in Kx,y\), K algebraically closed. Let \(\Gamma\) be the value semigroup of C, n be an integer and \(A_ n=\{0=a_ 0<a_ 1<...<a_{n- 1}\}=\{\min \Gamma \cap \{k+n{\mathbb{Z}}_{\geq 0}\}| k=0,...,n-1\}\) the Apéry basis of \(\Gamma\) relative to n. Let \(h\in Kx,y\) such that the intersection multiplicity \((f\cdot h)=\dim_ KKx,y/(f,h)\) is an element of \(A_ n\), \(n=ord_ xf(x,0)\). Then the author proves a factorization theorem for h with certain precise combinatorial statements about numerical invariants of the factors and numerical invariants of f. This theorem applies to h being a generic polar of f and some results of \textit{Merle} and \textit{Ephraim} turn out to be special cases of the factorization theorem of the author.
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 13F25
zbMATH DE Number: 4202467
zbMATH Keywords: Apéry basis of value semigroup
zbMATH Keywords: plane algebroid curve singularity
author: Ángel Granja
reviewed by: Gert-Martin Greuel
MaRDI profile type: Publication
full work available at URL: pjm.1989.140.85
OpenAlex ID: W1966183341
DOI: 10.2140/PJM.1989.140.85
description: scientific article; zbMATH DE number 4202467