The structure of the Prym map
type: Item
instance of: scholarly article
title: The structure of the Prym map
zbMATH Open document ID: 0538.14019
DOI: 10.1007/BF02392458
author: Roy Campbell Smith
author: Ron Donagi
published in: Acta Mathematica
publication date: 1981-01-01T00:00:00Z
review text: The paper under review is a detailed treatment of the result, announced by the authors in Journées géométrie algébrique, Angers 1979, 143-155 (1980; Zbl 0464.14015) that the degree of the Prym map \(P: {\mathcal R}_ 6\to {\mathcal A}_ 5\) is 27, where \({\mathcal R}_ g\) (for \(g=6)\) is a moduli space of unramified double covers of smooth genus g curves. The main idea is to investigate the fiber over a general Jacobian, which can be found explicitly. To compute the degree near a non-zerodimensional fiber the authors use the infinitesimal investigation, which was generously outlined for them by \textit{C. H. Clemens}. Since then \textit{V. Kanev} [Izv. Akad. Nauk SSSR, Ser. Mat. 46, 244-268 (1982)] has improved these methods and established that the degree of the Prym map \(P: {\mathcal R}_ g\to {\mathcal A}_{g-1}\) is one if \(g=9\); for \(g=7\) and 8 it is also one [\textit{R. Friedman} and \textit{R. Smith}, Invent. Math. 67, 473-490 (1982; Zbl 0506.14042)].
Mathematics Subject Classification ID: 14H15
Mathematics Subject Classification ID: 14H40
Mathematics Subject Classification ID: 14B25
Mathematics Subject Classification ID: 14K30
zbMATH DE Number: 3855277
zbMATH Keywords: Jacobian variety
zbMATH Keywords: general Torelli theorem
zbMATH Keywords: moduli space of unramified double covers of smooth curves
zbMATH Keywords: degree of the Prym map
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02392458
OpenAlex ID: W2000205172
description: scientific article; zbMATH DE number 3855277