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October 2021 On the Prym map of Galois coverings
Abolfazl Mohajer
Rocky Mountain J. Math. 51(5): 1793-1805 (October 2021). DOI: 10.1216/rmj.2021.51.1793

Abstract

We consider the Prym variety P(C˜C) associated to a Galois coverings of curves f:C˜C branched at r points. We discuss some properties and equivalent definitions and then consider the Prym map 𝒫=𝒫(G,g,r):R(G,g,r)Ap,δ with δ the type of the polarization. For Galois coverings whose Galois group is abelian and metabelian (nonabelian) we show that the differential of this map at certain points is injective. We also consider the Abel-Prym map u:C˜P(C˜C) and prove some results for its injectivity. In particular, we show that in contrast to the classical and cyclic case, the behavior of this map here is more complicated. The theories of abelian and metabelian Galois coverings play a substantial role in our analysis and have been used extensively throughout the paper.

Citation

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Abolfazl Mohajer. "On the Prym map of Galois coverings." Rocky Mountain J. Math. 51 (5) 1793 - 1805, October 2021. https://doi.org/10.1216/rmj.2021.51.1793

Information

Received: 6 January 2021; Revised: 16 March 2021; Accepted: 29 March 2021; Published: October 2021
First available in Project Euclid: 17 February 2022

Digital Object Identifier: 10.1216/rmj.2021.51.1793

Subjects:
Primary: 14H30 , 14H40

Keywords: Galois covering , Prym map , Prym variety

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 5 • October 2021
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