# Prym varieties and their moduli

• ### Gavril Farkas

Humboldt-Universität zu Berlin, Germany

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## Abstract

This survey discusses the geometry of the moduli space of Prym varieties. Several applications of Prym in algebraic geometry are presented. The paper begins with with a historical discussion of the life and achievements of Friedrich Prym. Topics treated in subsequent sections include singularities and Kodaira dimension of the moduli space, syzygies of Prym-canonical embedding and the geometry of the moduli space $\mathcal{R}_g$ in small genus.