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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Claire Voisin
Title: Hodge theory and complex algebraic geometry I, II
Additional book information: Vol. I, Cambridge University Press, New York, 2002, ix+322 pp., ISBN 0-521-80260-1, £65; 2003, xi+351 pp., ISBN 0-521-80283-0, £65

References [Enhancements On Off] (What's this?)

  • Georges de Rham, Differentiable manifolds, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 266, Springer-Verlag, Berlin, 1984. Forms, currents, harmonic forms; Translated from the French by F. R. Smith; With an introduction by S. S. Chern. MR 760450, DOI 10.1007/978-3-642-61752-2
  • M. Green, J. Murre, and C. Voisin, Algebraic cycles and Hodge theory, Lecture Notes in Mathematics, vol. 1594, Springer-Verlag, Berlin, 1994. Lectures given at the Second C.I.M.E. Session held in Torino, June 21–29, 1993; Edited by A. Albano and F. Bardelli. MR 1335238, DOI 10.1007/b52495
  • Claire Voisin, Théorie de Hodge et géométrie algébrique complexe, Cours Spécialisés [Specialized Courses], vol. 10, Société Mathématique de France, Paris, 2002 (French). MR 1988456, DOI 10.1017/CBO9780511615344
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    Review Information:

    Reviewer: Herbert Clemens
    Affiliation: Ohio State University
    Email: clemens@math.ohio-state.edu
    Journal: Bull. Amer. Math. Soc. 42 (2005), 507-520
    Published electronically: April 7, 2005
    Review copyright: © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.