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Theta divisors of generalized Prym varieties. I. (English) Zbl 0575.14037
Algebraic geometry, Proc. Conf., Sitges (Barcelona)/Spain 1983, Lect. Notes Math. 1124, 166-215 (1985).
[For the entire collection see Zbl 0551.00002.]
A generalization of the concept of Prym varieties is given by A. N. Tjurin [Russ. Math. Surv. 27(1972), No.5, 1-53 (1973); translation from Usp. Mat. Nauk 27, No.5(167), 3-50 (1972; Zbl 0256.14019)]. In this paper, the author investigates some fundamental properties of the generalized Prym varieties, especially the relationships between the principal polarization of the Prym variety and the original curve. These are given by the explicit calculation of the period matrix of the generalized Prym variety, but for the classical Prym varieties these are given intrinsically by D. Mumford [Contribut. to Analysis; Collect. of Papers dedic. L. Bers, 325-350 (1974; Zbl 0299.14018)].
Reviewer: T.Sekiguchi

14K25 Theta functions and abelian varieties
14H40 Jacobians, Prym varieties
14K30 Picard schemes, higher Jacobians