English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we consider the Prym variety $P(\widetilde{C}/C)$ associated toa Galois coverings of curves $f:\widetilde{C}\to C$ branched at $r$ points. Wediscuss some properties and equivalent definitions and then consider the Prymmap $\mathcal{P}=\mathcal{P}(G,g,r):R(G,g,r)\to A_{p,\delta}$ with $\delta$ thetype of the polarization. For Galois coverings whose Galois group is abelianand metabelian (non-abelian) we show that the differential of this map atcertain points is injective. We also consider the Abel-Prym map$u:\widetilde{C}\to P(\widetilde{C}/C)$ and prove some results for itsinjectivity. In particular we show that in contrast to the classical and cycliccase, the behavior of this map here is more complicated. The theories ofabelian and metabelian Galois coverings play a substantial role in our analysisand have been used extensively throughout the paper.

On the Prym map of Galois covering