Degree of irrationality of abelian surfaces
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.
scientific article; zbMATH DE number 783907