Modular curves and Poncelet polygons
type: Item
instance of: scholarly article
title: Modular curves and Poncelet polygons
zbMATH Open document ID: 0789.14033
DOI: 10.1007/BF01444875
author: V. Pereyra
published in: Mathematische Annalen
publication date: 1994-06-20T00:00:00Z
full work available at URL: https://eudml.org/doc/165030
review text: A Poncelet-polygon is a polygon in the projective plane (over \(\mathbb{C})\) with its vertices on one smooth conic while its sides touch another smooth conic. It is well-known that Poncelet-\(n\)-gons are related to \(n\)- torsion elements in elliptic curves. We consider moduli of this situation and obtain a plane model for the modular curve parametrizing elliptic curves with a level-2-structure on an \(n\)-torsion point. Using this plane curve we compute numbers for Poncelet-configurations in a pencil of conics and for pairs of conics which are mutually related by Poncelet- polygons.
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 51N15
Mathematics Subject Classification ID: 14G35
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14N10
zbMATH DE Number: 537240
zbMATH Keywords: Poncelet-polygon
zbMATH Keywords: modular curve
MaRDI profile type: Publication
cites work: Q5749404
cites work: On Cayley's explicit solution to Poncelet's porism
cites work: On compact complex analytic surfaces. I
description: scientific article; zbMATH DE number 537240