On some one parameter families of genus 2 algebraic curves and half twists
type: Item
instance of: scholarly article
title: On some one parameter families of genus 2 algebraic curves and half twists
zbMATH Open document ID: 1109.30035
DOI: 10.4171/CMH/97
author: R. Silhol
published in: Commentarii Mathematici Helvetici
publication date: 2007-04-26T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_issue.php
review text: Summary: We show that for certain families of surfaces in genus 2 there is an action of \(\text{PSL}_2(\mathbb Z)\) that can be expressed very naturally both in terms of Fenchel-Nielsen coordinates for the surfaces and in terms of equations of the associated algebraic curves. We also show that one of these families coincides with the \(\text{SL}_2(\mathbb R)\) orbit of the translation surface tiled by three squares and that the above \(\text{PSL}_2(\mathbb Z)\) action is exactly induced by the natural action of \(\text{SL}_2(\mathbb R)\)) on this orbit.
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 14H15
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 30F30
zbMATH DE Number: 5146412
zbMATH Keywords: hyperbolic surfaces
zbMATH Keywords: algebraic curves
zbMATH Keywords: translation surfaces
zbMATH Keywords: Teichmüller spaces
zbMATH Keywords: uniformization
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5146412