Prym varieties of cyclic coverings

TL;DR

This paper studies the Prym map associated with cyclic coverings of algebraic curves, demonstrating its generic finiteness in most cases and determining the dimension of its image, thus advancing understanding of Prym varieties in algebraic geometry.

Contribution

It establishes the generic finiteness of the Prym map for cyclic coverings and computes the dimension of its image, providing new insights into Prym varieties.

Findings

Prym map is generically finite in most cases.

Dimension of the Prym map's image is explicitly determined.

Advances understanding of the structure of Prym varieties.

Abstract

The Prym map of type (g,n,r) associates to every cyclic covering of degree n of a curve of genus g, ramified at a reduced divisor of degree r, the corresponding Prym variety. We show that the corresponding map of moduli spaces is generically finite in most cases. From this we deduce the dimension of the image of the Prym map.