Prym varieties of double coverings of elliptic curves

TL;DR

This paper proves that the Prym map for double coverings of elliptic curves is generically injective and is birational when ramified at six points, advancing understanding of Prym varieties in algebraic geometry.

Contribution

It establishes the generic injectivity of the Prym map for double coverings of elliptic curves and shows it is birational for six ramification points, a new result in the field.

Findings

Prym map is generically injective for r>4

The Prym map is birational when r=6

Advances understanding of Prym varieties of elliptic curves

Abstract

We prove the generic injectivity of the Prym map, sending a double covering of an elliptic curve ramified at r>4 points to its polarized Prym variety. For r=6 the map is birational.