Degree of irrationality of abelian surfaces
type: Item
instance of: scholarly article
title: Degree of irrationality of abelian surfaces
zbMATH Open document ID: 0837.14009
author: Hisao Yoshihara
author: Hiro-O Tokunaga
published in: Journal of Algebra
publication date: 1996-05-20T00:00:00Z
review text: The degree of rationality of an algebraic variety \(V\) is defined as the lowest degree of a generically finite dominant rational map from \(V\) to a rational variety. It is known that the degree of rationality of an abelian surface is at least 3. This article is devoted to the construction of examples of abelian surfaces with degree of rationality 3. One of them is \(E \times E\), where \(E\) is the elliptic curve \(y^2 = x^3 - 1\) (and it is shown to be the only case where the degree 3 rational map onto \(\mathbb{P}^2\) is Galois). Abelian surfaces that contain a smooth genus 3 curve are also shown to have degree of rationality 3. An explicit family of principally polarized surfaces having this property is given.
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14M20
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 14K05
zbMATH DE Number: 783907
zbMATH Keywords: degree of rationality
zbMATH Keywords: dominant rational map
zbMATH Keywords: rational variety
zbMATH Keywords: abelian surfaces
zbMATH Keywords: principally polarized surfaces
MaRDI profile type: Publication
full work available at URL: jabr.1995.1170
OpenAlex ID: W1985940139
DOI: 10.1006/JABR.1995.1170
description: scientific article; zbMATH DE number 783907