Le théorème de Torelli pour les intersections de trois quadriques. (Torelli theorem for intersections of three quadrics) (Q917631)

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)].