Plane curves whose singular points are cusps and triple coverings of \(\mathbb{P}^2\)
type: Item
instance of: scholarly article
title: Plane curves whose singular points are cusps and triple coverings of \(\mathbb{P}^2\)
zbMATH Open document ID: 0708.14017
DOI: 10.1007/BF01160117
author: Hisao Yoshihara
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155403
review text: Let \(C\) be an algebraic plane curve in the complex projective plane \(\mathbb{P}^2\); assume that \(C\) has degree \(d\in 3\mathbb{Z}\) and, furthermore, that its only singular points are unibranched double or triple points. The author finds an inequality relating some invariants of the singular points of \(C\), obtained from their multiplicities and maximal contacts, and the degree d of the curve. The proof uses triple coverings of \(\mathbb{P}^2\) branched along \(C\) and some of them give examples of minimal surfaces of general type.
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 14J29
zbMATH DE Number: 4163055
zbMATH Keywords: cusps
zbMATH Keywords: multiplicities
zbMATH Keywords: maximal contacts
zbMATH Keywords: degree
zbMATH Keywords: triple coverings
zbMATH Keywords: minimal surfaces of general type
reviewed by: Eduardo Casas-Alvero
MaRDI profile type: Publication
cites work: Some examples of algebraic surfaces
cites work: Pluricanonical systems on algebraic surfaces of general type
cites work: On the Structure of Complex Analytic Surfaces, IV
cites work: Normal Two-Dimensional Singularities. (AM-71)
cites work: Triple Covers in Algebraic Geometry
cites work: On a generalization of complete intersections
cites work: Double coverings and surfaces of general type
cites work: Plane Curves Whose Singular Points are Cusps
cites work: The degree of rational cuspidal curves
description: scientific article; zbMATH DE number 4163055