The structure of algebraic threefolds: an introduction to Mori's program
Author:
János Kollár
Journal:
Bull. Amer. Math. Soc. 17 (1987), 211273
MSC (1985):
Primary 1402, 14E30, 14E35, 32J25, 14J10, 14J15, 14E05, 14J30
MathSciNet review:
903730
Fulltext PDF
References 
Similar Articles 
Additional Information

C.
Herbert Clemens, A scrapbook of complex curve theory, Plenum
Press, New York, 1980. The University Series in Mathematics. MR 614289
(82i:14001)

William
Fulton, Algebraic curves. An introduction to algebraic
geometry, W. A. Benjamin, Inc., New YorkAmsterdam, 1969. Notes
written with the collaboration of Richard Weiss; Mathematics Lecture Notes
Series. MR
0313252 (47 #1807)

David
Mumford, Algebraic geometry. I, SpringerVerlag, Berlin, 1976.
Complex projective varieties; Grundlehren der Mathematischen
Wissenschaften, No. 221. MR 0453732
(56 #11992)

Miles
Reid, Undergraduate algebraic geometry, London Mathematical
Society Student Texts, vol. 12, Cambridge University Press, Cambridge,
1988. MR
982494 (90a:14001)

Algebraic geometry. I, Encyclopaedia of Mathematical Sciences,
vol. 23, SpringerVerlag, Berlin, 1994. Algebraic curves. Algebraic
manifolds and schemes; A translation of Current problems in mathematics.
Fundamental directions, Vol. 23 (Russian), Akad. Nauk SSSR, Vsesoyuz.
Inst.\
Nauchn. i Tekhn. Inform., Moscow, 1988; Translation by D. Coray and
V. N. Shokurov; Translation edited by I. R. Shafarevich. MR 1287418
(95b:14001)

C. L. Siegel, Topics in complex function theory. I, II, III, WileyInterscience, 1969. A beautiful introduction to the analytic theory of Riemann surfaces.

W.
Barth, C.
Peters, and A.
Van de Ven, Compact complex surfaces, Ergebnisse der
Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related
Areas (3)], vol. 4, SpringerVerlag, Berlin, 1984. MR 749574
(86c:32026)

Phillip
Griffiths and Joseph
Harris, Principles of algebraic geometry, WileyInterscience
[John Wiley & Sons], New York, 1978. Pure and Applied Mathematics. MR 507725
(80b:14001)

Robin
Hartshorne, Algebraic geometry, SpringerVerlag, New York,
1977. Graduate Texts in Mathematics, No. 52. MR 0463157
(57 #3116)

Kenji
Ueno, Classification theory of algebraic varieties and compact
complex spaces, Lecture Notes in Mathematics, Vol. 439,
SpringerVerlag, Berlin, 1975. Notes written in collaboration with P.
Cherenack. MR
0506253 (58 #22062)

C. H. Clemens, Curves on threefolds, the AbelJacobi 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.)

Yujiro
Kawamata, Katsumi
Matsuda, and Kenji
Matsuki, Introduction to the minimal model problem, Algebraic
geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10,
NorthHolland, Amsterdam, 1987, pp. 283–360. MR 946243
(89e:14015)

Shigefumi
Mori, Classification of higherdimensional varieties,
Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) Proc. Sympos.
Pure Math., vol. 46, Amer. Math. Soc., Providence, RI, 1987,
pp. 269–331. MR 927961
(89a:14040)

Miles
Reid, Tendencious survey of 3folds, Algebraic geometry,
Bowdoin, 1985 (Brunswick, Maine, 1985) Proc. Sympos. Pure Math.,
vol. 46, Amer. Math. Soc., Providence, RI, 1987,
pp. 333–344. MR 927962
(89h:14033)

Miles
Reid, Young person’s guide to canonical singularities,
Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) Proc. Sympos.
Pure Math., vol. 46, Amer. Math. Soc., Providence, RI, 1987,
pp. 345–414. MR 927963
(89b:14016)

P.
M. H. Wilson, Towards birational classification of algebraic
varieties, Bull. London Math. Soc. 19 (1987),
no. 1, 1–48. MR 865038
(87m:14038), http://dx.doi.org/10.1112/blms/19.1.1
 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, WileyInterscience, 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, WileyInterscience, 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 AbelJacobi 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 higherdimensional 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 threedimensional terminal singularities. MR 927963
 P. M. H. Wilson, Towards birational classification of algebraic varieties, Bull. London Math. Soc. 19 (1987), 148. Detailed survey aimed at the general algebraic geometer. MR 865038
Similar Articles
Retrieve articles in Bulletin of the American Mathematical Society
with MSC (1985):
1402,
14E30,
14E35,
32J25,
14J10,
14J15,
14E05,
14J30
Retrieve articles in all journals
with MSC (1985):
1402,
14E30,
14E35,
32J25,
14J10,
14J15,
14E05,
14J30
Additional Information
DOI:
http://dx.doi.org/10.1090/S027309791987155480
PII:
S 02730979(1987)155480
