Stability of pencils of plane curves, log canonical thresholds and multiplicities

2021/01/05 by Aline Zanardini, Zanardini, Aline
Mathematics · #14E99 (Secondary) #14L24 (Primary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2101.01756

openalex publication_date 2021/01/05 · openalex created_date 2021/01/18 · openalex updated_date 2026/07/28

Abstract

In this paper we study the problem of classifying pencils of curves of degree d in ℙ² using geometric invariant theory. We consider the action of SL(3) and we relate the stability of a pencil to the stability of its generators, to the log canonical threshold of its members, and to the multiplicities of its base points, thus obtaining explicit stability criteria.

Citations

• Explicit Constructions of Halphen Pencils

Related

• Stability of pencils of plane sextics and Halphen pencils of index two
• Log canonical thresholds of high multiplicity reduced plane curves
• Pencils and critical locus on normal surfaces
• Linear pencils on graphs and on real curves
• Worst singularities of plane curves of given degree