Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

 

 

The structure of algebraic threefolds: an introduction to Mori's program


Author: János Kollár
Journal: Bull. Amer. Math. Soc. 17 (1987), 211-273
MSC (1985): Primary 14-02, 14E30, 14E35, 32J25, 14J10, 14J15, 14E05, 14J30
MathSciNet review: 903730
Full-text PDF

References | Similar Articles | Additional Information

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

  • C. H. Clemens, A scrapbook of complex curve theory, Plenum Press, 1980. Elementary, unusual, and beautiful introduction to curves. MR 614289
  • W. Fulton, Algebraic curves, W. A. Benjamin, 1969. Leisurely algebraic introduction to curves. MR 313252
  • D. Mumford, Algebraic geometry I: Complex projective varieties, Springer, 1976. Using a little commutative algebra, this is the fastest way to interesting theorems. Part II does not exist. MR 453732
  • M. Reid, Undergraduate algebraic geometry, London Math. Soc. Texts in Math. (to appear). The most elementary introduction to the general theory. MR 982494
  • I. R. Shafarevich, Basic algebraic geometry, Springer, 1977. Parts I and II provide a peaceful algebraic introduction. Part III is an essentially independent glimpse at compact complex manifolds. MR 1287418
  • C. L. Siegel, Topics in complex function theory. I, II, III, Wiley-Interscience, 1969. A beautiful introduction to the analytic theory of Riemann surfaces.
  • W. Barth, C. Peters and A. Van de Ven, Compact complex surfaces, Springer, 1984. Comprehensive and elegant treatment of surfaces. MR 749574
  • P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley-Interscience, 1978. A long and thorough introduction to the analytic theory of algebraic varieties. MR 507725
  • R. Hartshorne, Algebraic geometry, Springer, 1977. This is the standard algebraic introduction. MR 463157
  • K. Ueno, Classification theory of algebraic varieties and compact complex spaces, Lecture Notes in Math., vol. 439, Springer, 1975. An overview prior to Mori's work. MR 506253
  • C. H. Clemens, Curves on threefolds, the Abel-Jacobi mapping, Proc. Sympos. Pure Math. (Algebraic Geometry, Bowdoin College, 1985), Amer. Math. Soc., to appear. Detailed study of the geometry of special threefolds. (The other point of view from Chapter 8.)
  • Y. Kawamata, K. Matsuda and K. Matsuki, Introduction to the minimal model problem, Adv. Studies in Pure Math., Sendai, to appear. Comprehensive survey, aimed at experts. MR 946243
  • S. Mori, Classification of higher-dimensional varieties, Proc. Sympos. Pure Math. (Algebraic Geometry, Bowdoin College, 1985), Amer. Math. Soc., to appear. Mostly about results not encompassed by Mori's program. MR 927961
  • M. Reid, Tendencious survey of 3 -folds, Proc. Sympos. Pure Math. (Algebraic Geometry, Bowdoin College, 1985), Amer. Math. Soc., to appear. Mostly philosophy and jokes. Recommended for algebraic geometers. MR 927962
  • M. Reid, Young person's guide to canonical singularities, Proc. Sympos. Pure Math. (Algebraic Geometry, Bowdoin College, 1985), Amer. Math. Soc., to appear. Excellent introduction to three-dimensional terminal singularities. MR 927963
  • P. M. H. Wilson, Towards birational classification of algebraic varieties, Bull. London Math. Soc. 19 (1987), 1-48. Detailed survey aimed at the general algebraic geometer. MR 865038

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 14-02, 14E30, 14E35, 32J25, 14J10, 14J15, 14E05, 14J30

Retrieve articles in all journals with MSC (1985): 14-02, 14E30, 14E35, 32J25, 14J10, 14J15, 14E05, 14J30


Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1987-15548-0