Algebraic geometry. III. Complex algebraic varieties, algebraic curves and their Jacobians. Transl. from the Russian by I. Rivin
type: Item
instance of: scholarly article
title: Algebraic geometry. III. Complex algebraic varieties, algebraic curves and their Jacobians. Transl. from the Russian by I. Rivin
zbMATH Open document ID: 0886.14001
published in: Encyclopaedia of Mathematical Sciences
publication date: 1998-01-26T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 14-02
Mathematics Subject Classification ID: 14H40
Mathematics Subject Classification ID: 14C34
Mathematics Subject Classification ID: 32G20
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 00B50
zbMATH DE Number: 1110137
zbMATH Keywords: Algebraic geometry
zbMATH Keywords: Complex algebraic varieties
zbMATH Keywords: Algebraic curves
zbMATH Keywords: Jacobians
zbMATH Keywords: Torelli theorems
zbMATH Keywords: Hodge theory
zbMATH Keywords: period maps
zbMATH Keywords: degeneration
zbMATH Keywords: algebraic curves
zbMATH Keywords: Prym varieties
zbMATH Keywords: theta functions
zbMATH Keywords: Schottky problem
reviewed by: Werner Kleinert
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1110137