Parshin, A. N. (ed.); Shafarevich, I. R. (ed.); Gamkrelidze, R. V. (ed.) Algebraic geometry. III. Complex algebraic varieties, algebraic curves and their Jacobians. Transl. from the Russian by I. Rivin. (English) Zbl 0886.14001 Encyclopaedia of Mathematical Sciences. 36. Berlin: Springer. 270 p. (1998). Show indexed articles as search result. The articles of this volume are translations from the series Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 36 (1989; Zbl 0683.00008).The first part of this EMS (= Encyclopaedia of Mathematical Sciences) volume is the fairly literal translation of the survey article “Complex algebraic manifolds: Periods of integrals, Hodge structures” by V. S. Kulikov and P. F. Kurchanov, whose Russian original had been reviewed, a few years ago, in great detail [pp. 5-231 of the cited volume (1989; Zbl 0753.14003)].The analogous statement applies to the second part, which is the translation of the survey treatise “Algebraic curves and their Jacobians” by V. V. Shokurov, the Russian original of which had been reviewed, in just as detailed a manner [see pp. 233-273 of the Russian volume (1989; Zbl 0735.14023)].Although these two surveys of encyclopaedic character had been written almost ten years ago, their timeless excellence has maintained its spreading significance for the general education within the mathematical community as well as its essentially up-to-date reference character. Reviewer: W.Kleinert (Berlin) Cited in 1 Document MSC: 14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry 14H40 Jacobians, Prym varieties 14C34 Torelli problem 32G20 Period matrices, variation of Hodge structure; degenerations 14C30 Transcendental methods, Hodge theory (algebro-geometric aspects) 00B50 Collections of translated articles of general interest Keywords:Algebraic geometry; Complex algebraic varieties; Algebraic curves; Jacobians; Torelli theorems; Hodge theory; period maps; degeneration; algebraic curves; Prym varieties; theta functions; Schottky problem Citations:Zbl 0683.00008; Zbl 0753.14003; Zbl 0735.14023 PDFBibTeX XMLCite \textit{A. N. Parshin} (ed.) et al., Algebraic geometry. III. Complex algebraic varieties, algebraic curves and their Jacobians. Transl. from the Russian by I. Rivin. Berlin: Springer (1998; Zbl 0886.14001)