Algebraic geometry. III. Complex algebraic varieties, algebraic curves and their Jacobians. Transl. from the Russian by I. Rivin (Q1377902): Difference between revisions

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 \textit{V. S. Kulikov} and \textit{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 \textit{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.