A note on the stability of pencils of plane curves
type: Item
instance of: scholarly article
title: A note on the stability of pencils of plane curves
zbMATH Open document ID: 1482.14048
author: Aline Zanardini
published in: Mathematische Zeitschrift
publication date: 2022-01-21T00:00:00Z
review text: The semisimple group \(PGL(3)\) acts on the set of all degree \(d\) complex plane curves and on the set of all pencils of degree \(d\) plane curves. The author uses the log canonical threshold to give explicit criteria for the stability or semistability of a pencil \(P\) in terms of the stability or semistability of its members. The pencil \(P\) is semistable (resp. stable) if all its members \(C_d\in P\) are semistable (resp. stable). The pencil \(P\) is stable if all its members are semistable and at most one \(C_d\in P\) is strictly semistable. The author gives a criterion for the stability of \(P\) when \(2\) of its members are strictly semistable.
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 14H10
zbMATH DE Number: 7461064
zbMATH Keywords: GIT stability
zbMATH Keywords: log canonical threshold
zbMATH Keywords: pencils of plane curves
MaRDI profile type: Publication
full work available at URL: s00209-021-02857-w
OpenAlex ID: W3197732642
cites work: Q3337582
cites work: Worst singularities of plane curves of given degree
cites work: Q4780265
cites work: Compact moduli of plane curves
cites work: Log canonical thresholds of semistable plane curves
cites work: Polynomials with integral coefficients, equivalent to a given polynomial
cites work: Singularities of Pairs
cites work: Q5387334
cites work: On the Stability of Pencils of Cubic Curves
DOI: 10.1007/S00209-021-02857-W
description: scientific article; zbMATH DE number 7461064