A pencil in \({\widetilde {\mathcal M}}_ 6\) with three points at the boundary
type: Item
instance of: scholarly article
title: A pencil in \({\widetilde {\mathcal M}}_ 6\) with three points at the boundary
zbMATH Open document ID: 0758.14013
DOI: 10.1007/BF02414065
author: V. Gonzalez-Aguilera
author: Rubí E. Rodríguez
published in: Geometriae Dedicata
publication date: 1992-09-27T00:00:00Z
review text: The authors show that the pencil of plane sextics \(\{C_ t=W+tD\}\), \(t\in\mathbb{P}^ 1\), where \(W\) is the known (since 1895) Wiman sextic and \(D:xyz(x-y)(x-z)(y-z)=0\), now called Dolgachev sextic, is such that \(\text{Aut}(C_ t)={\mathfrak A}_ 5\), the alternating group, for all \(t\in\mathbb{P}^ 1\). Then they show that the image of this pencil in \(\tilde{\mathcal M}_ 6\), the moduli space of stable curves of genus six, touches the boundary in exactly three points, and they describe the corresponding curves as divisors on the Del Pezzo surface of degree 5.
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14C21
Mathematics Subject Classification ID: 14E07
zbMATH DE Number: 58793
zbMATH Keywords: automorphism group of sextic
zbMATH Keywords: pencil of plane sextic
zbMATH Keywords: Wiman's sextic
zbMATH Keywords: Dolgachev sextic
reviewed by: A. Del Centina
MaRDI profile type: Publication
cites work: Q3808217
cites work: Q5343413
cites work: Q4402061
full work available at URL: https://doi.org/10.1007/bf02414065
OpenAlex ID: W2938103810
description: scientific article; zbMATH DE number 58793