Kanev, V. I. The global Torelli theorem for Prym varieties at a generic point. (English. Russian original) Zbl 0566.14014 Math. USSR, Izv. 20, 235-257 (1983); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 46, No. 2, 244-268 (1982). Let \(R_ g\) be a moduli space of unramified double covers of smooth genus g curves and \(A_{g-1}\) be a moduli space of principally polarized Abelian varieties of dimension g-1. The paper under review investigates the Prym map \(P: R_ g\to A_{g-1}\). The author establishes here a generic Torelli theorem for the Prym map with \(g\geq 8\), i.e. that the Prym map is a birational imbedding when \(g\geq 8\). The proof is an improvement on the methods used by R. Donagi and R. C. Smith in Acta Math. 146, 25-102 (1981; Zbl 0538.14019). Independently, R. Friedman and R. Smith have proved the same result for \(g\geq 7\) [Invent. Math. 67, 473-490 (1982; Zbl 0506.14042)]. Recently, Friedman proved the generic Torelli theorem for intersections of three quadrics, which is equivalent to the generic Torelli theorem for the Prym map on some subspace in \(R_ g\). A conjectural description of the fibers for the Prym map P is given by R. Donagi in Bull. Am. Math. Soc., New Ser. 4, 181-185 (1981; Zbl 0491.14016). Reviewer: V.V.Shokurov Cited in 2 ReviewsCited in 6 Documents MSC: 14H10 Families, moduli of curves (algebraic) 14B25 Local structure of morphisms in algebraic geometry: étale, flat, etc. 14D20 Algebraic moduli problems, moduli of vector bundles 14E05 Rational and birational maps Keywords:moduli space of curves; unramified double covers; principally polarized Abelian varieties; Prym map; generic Torelli theorem Citations:Zbl 0538.14019; Zbl 0506.14042; Zbl 0491.14016 PDFBibTeX XMLCite \textit{V. I. Kanev}, Math. USSR, Izv. 20, 235--257 (1983; Zbl 0566.14014); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 46, No. 2, 244--268 (1982) Full Text: DOI