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Book Review

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Book Information:

Author: Robert Lazarsfeld
Title: Positivity in algebraic geometry. I-II
Additional book information: Vol. I, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, Springer-Verlag, Berlin, 2004, xviii+ 387 pp., ISBN 3-540-22533-1; xviii+385 pp., ISBN 3-540-22534-X, US$129.00, hardcover; US$34.95, softcover

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

  • [Deb01] Olivier Debarre, Higher-dimensional algebraic geometry, Universitext, Springer-Verlag, New York, 2001. MR 1841091
  • [GY86] L. Zhiyong Gao and S.-T. Yau, The existence of negatively Ricci curved metrics on three-manifolds, Invent. Math. 85 (1986), no. 3, 637–652. MR 848687, https://doi.org/10.1007/BF01390331
  • [KM98] János Kollár and Shigefumi Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, vol. 134, Cambridge University Press, Cambridge, 1998. With the collaboration of C. H. Clemens and A. Corti; Translated from the 1998 Japanese original. MR 1658959
  • [Laz04a] Robert Lazarsfeld, Positivity in algebraic geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 48, Springer-Verlag, Berlin, 2004. Classical setting: line bundles and linear series. MR 2095471
    Robert Lazarsfeld, Positivity in algebraic geometry. II, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 49, Springer-Verlag, Berlin, 2004. Positivity for vector bundles, and multiplier ideals. MR 2095472
  • [Laz04b] Robert Lazarsfeld, Positivity in algebraic geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 48, Springer-Verlag, Berlin, 2004. Classical setting: line bundles and linear series. MR 2095471
    Robert Lazarsfeld, Positivity in algebraic geometry. II, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 49, Springer-Verlag, Berlin, 2004. Positivity for vector bundles, and multiplier ideals. MR 2095472
  • [Mat02] Kenji Matsuki, Introduction to the Mori program, Universitext, Springer-Verlag, New York, 2002. MR 1875410
  • [Sul04] Dennis Sullivan, René Thom’s work on geometric homology and bordism, Bull. Amer. Math. Soc. (N.S.) 41 (2004), no. 3, 341–350. MR 2058291, https://doi.org/10.1090/S0273-0979-04-01026-2

Review Information:

Reviewer: János Kollár
Affiliation: Princeton University
Email: kollar@math.princeton.edu
Journal: Bull. Amer. Math. Soc. 43 (2006), 279-284
Published electronically: February 16, 2006
Review copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.