Le théorème de Torelli pour les intersections de trois quadriques. (Torelli theorem for intersections of three quadrics)
type: Item
instance of: scholarly article
title: Le théorème de Torelli pour les intersections de trois quadriques. (Torelli theorem for intersections of three quadrics)
zbMATH Open document ID: 0705.14029
DOI: 10.1007/BF01393887
author: Olivier Debarre
published in: Inventiones Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143663
review text: The following result is established: Every isomorphism between the Prym varieties of two admissible [in the sense of \textit{A. Beauville}, Invent. Math. 41, 149-196 (1977; Zbl 0333.14013)] coverings of stable plane curves of the same degree \(= 7\) (one of which satisfies a mild technical condition) is induced by an isomorphism between these coverings. - It follows that if two complete intersections of three quadrics of odd dimension are given, then any isomorphism between their generalized jacobians is induced, modulo sign, by an isomorphism between them. - This provides a definitive completion of the results of \textit{R. Friedman} and \textit{R. Smith} [Invent. Math. 85, 615-635 (1986; Zbl 0619.14027)] valid generically. The author's methods are constructive, and make use of an idea of Welters introduced for the classical Torelli theorem, and later used for Prym varieties [\textit{G. E. Welters}, Am. J. Math. 109, 165-182 (1987; Zbl 0639.14026)].
Mathematics Subject Classification ID: 14H40
Mathematics Subject Classification ID: 14K30
Mathematics Subject Classification ID: 14C34
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 30F99
zbMATH DE Number: 4156637
zbMATH Keywords: Prym varieties
zbMATH Keywords: coverings of stable plane curves
zbMATH Keywords: complete intersections of three quadrics
zbMATH Keywords: Torelli theorem
MaRDI profile type: Publication
Wikidata QID: Q64115189
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description: scientific article; zbMATH DE number 4156637