Theta-duality on Prym varieties and a Torelli Theorem

TL;DR

This paper establishes theta-dual equalities in Prym varieties derived from unramified double coverings of curves and proves a Torelli-type theorem linking Prym varieties to the original curves.

Contribution

It proves schematic theta-dual equalities in Prym varieties and introduces a Torelli theorem connecting Prym varieties with the original curves.

Findings

Proved T(C')=V^2 and T(V^2)=C' in Prym varieties.

Established a Torelli theorem for Prym varieties.

Linked Prym varieties to the original curves via theta-dualities.

Abstract

Let p:C' -> C be an unramified double covering of irreducible smooth curves and let P be the attached Prym variety. We prove the schematic theta-dual equalities in the Prym variety T(C')=V^2 and T(V^2)=C', where V^2 is the Brill-Noether locus of P associated to p considered by Welters. As an application we prove a Torelli Theorem analogous to the fact that the g-th symmetric product of a curve D of genus g determines the curve.