When is a complex elliptic curve the product of two real algebraic curves?
type: Item
instance of: scholarly article
title: When is a complex elliptic curve the product of two real algebraic curves?
zbMATH Open document ID: 0734.14018
DOI: 10.1007/BF01444728
author: N. E. Zubov
published in: Mathematische Annalen
publication date: 1992-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164969
review text: Recall that a complex projective variety \(V\subseteq {\mathbb{P}}^ n({\mathbb{C}})\) can be, in the obvious way, considered as a real algebraic variety and, as such, will be denoted by \(V_{{\mathbb{R}}}\). Moreover, it can be shown that \(V_{{\mathbb{R}}}\) is an affine real algebraic variety, by which we mean a locally ringed space isomorphic to an algebraic subset of \({\mathbb{R}}^ n\), for some n, equipped with the sheaf of \({\mathbb{R}}\)-valued regular functions. - The paper contains the full answer to the following problem: Given a complex elliptic curve E, decide when the underlying real algebraic surface \(E_{{\mathbb{R}}}\) is biregularly isomorphic to the product of two real algebraic curves.
Mathematics Subject Classification ID: 14P05
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 4214200
zbMATH Keywords: complex elliptic curve as real algebraic surface
reviewed by: Johannes Huisman
MaRDI profile type: Publication
cites work: Real algebraic hypersurfaces in complex projective varieties
cites work: The underlying real algebraic structure of complex elliptic curves
cites work: Elliptic Curves
description: scientific article; zbMATH DE number 4214200