On degrees and birationality of the maps \(X_0(N)\to \mathbb P^2\) constructed via modular forms
type: Item
instance of: scholarly article
title: On degrees and birationality of the maps \(X_0(N)\to \mathbb P^2\) constructed via modular forms
zbMATH Open document ID: 1372.11057
author: Goran Muić
published in: Monatshefte für Mathematik
publication date: 2016-08-01T00:00:00Z
review text: In this paper, the author proves a nice formula relating the degree of a curve which is the image of a mapping constructed out of three linearly independent modular forms of the same integral or half-integral weight into the projective space and the degree of that map. Based on this formula, a criterion for the birationality of the map is obtained. As an application, the author gives a formula for the total degree, namely the degree considered as a polynomial of two (independent) variables of the classical modular polynomial. An interesting example is given on birationality which lead to a question on the existence of explicit models for modular curves.
reviewed by: Emre Alkan
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11F23
zbMATH DE Number: 6608241
zbMATH Keywords: modular forms
zbMATH Keywords: modular curves
zbMATH Keywords: birational equivalence
zbMATH Keywords: modular polynomial
describes a project that uses: SageMath
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: s00605-016-0908-y
OpenAlex ID: W2343413558
cites work: Q5625265
cites work: Modular polynomials via isogeny volcanoes
cites work: Q4920301
cites work: The Magma algebra system. I: The user language
cites work: Q4342000
cites work: Birational Maps of X(1) into P2
cites work: Modular curves and bases for the spaces of cuspidal modular forms
cites work: Defining equations of modular curves
cites work: Q4449110
cites work: Modular Forms
cites work: Q4697470
cites work: Basic Algebraic Geometry 1
cites work: On embeddings of modular curves in projective spaces
DOI: 10.1007/S00605-016-0908-Y
description: scientific article; zbMATH DE number 6608241