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Book Review
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Book Information
Author(s):
János Kollár and Shigefumi Mori, with the collaboration of C. H. Clemens and A. Corti
Title:
Birational geometry of algebraic varieties
Additional book information:
Cambridge University Press,
1998,
viii + 254,
0-521-63277-3
References:
-
- 1.
- D. Abramovich, K. Karu, K. Matsuki and J. W
odarczyk. Torification and factorization of birational maps. math.AG/9904135. - 2.
- V. Alexeev. Boundedness and
for log surfaces. Internat. J. Math. 5 (1994), 779-810. MR 95k:14048 - 3.
- T. Bridgeland. Flops and derived categories. math.AG/0009053.
- 4.
- F. Campana. Connexité rationnelle des variétés de Fano. Ann. Sci. École Norm. Sup. 25 (1992), 539-545. MR 93k:14050
- 5.
- A. Corti and M. Reid, eds. Explicit Birational Geometry of 3-Folds. Cambridge Univ. Press, 2000.
- 6.
- P. Francia. Some remarks on minimal models I. Compositio Math. 40 (1980), 301-313. MR 81h:14013
- 7.
- Y. Kawamata. On the classification of non-complete algebraic surfaces. Lecture Notes in Math. 732 (1979), Springer, 215-232. MR 81c:14021
- 8.
- Y. Kawamata. Elementary contractions of algebraic 3-folds. Ann. of Math. 119 (1984), 95-110. MR 86c:14013a
- 9.
- Y. Kawamata. Pluricanonical systems on minimal algebraic varieties. Invent. Math. 79 (1985), 567-588. MR 87h:14005
- 10.
- Y. Kawamata. The Zariski decomposition of log-canonical divisors. Proc. Symp. Pure Math. 46 (1987), Amer. Math. Soc., 425-433. MR 89b:14052
- 11.
- Y. Kawamata. Abundance theorem for minimal threefolds. Invent. Math. 108 (1992), 229-246. MR 93f:14012
- 12.
- J. Kollár, Y. Miyaoka and S. Mori. Rational connectedness and boundedness of Fano manifolds. J. Differential Geom. 36 (1992), 765-779. MR 94g:14021
- 13.
- Y. Miyaoka. On the Kodaira dimension of minimal threefolds. Math. Ann. 281 (1988), 325-332. MR 89g:14028
- 14.
- Y. Miyaoka. Abundance conjecture for 3-folds: case
. Compositio Math. 68 (1988), 203-220. MR 89m:14023 - 15.
- N. Nakayama. Invariance of the plurigenera of algebaic varieties under minimal model conjectures. Topology 25 (1986), 237-251. MR 87g:14034
- 16.
- H. Takagi. 3-fold log flips according to V. V. Shokurov. math.AG/9803145.
- 17.
- S. Tsunoda and M. Miyanishi. The structure of open algebraic surfaces II. Progress in Math. 39 (1983), Birkhäuser Boston, 499-544. MR 86c:14030
- 18.
- J. W
odarczyk. Birational cobordisms and factorization of birational maps. J. Algebraic Geom. 9 (2000), 425-449. CMP 2000:11 - 19.
- J. W
odarczyk. Toroidal varieties and the weak Factorization Theorem. math.AG/9904076.
Additional Information:
Reviewer(s):
Yujiro
Kawamata
Affiliation:
University of Tokyo
Email:
kawamata@ms.u-tokyo.ac.jp
Review Information:
Journal:
Bull. Amer. Math. Soc.
38
(2001),
267-272.
MSC
(2000):
Primary 14E30
DOI:
10.1090/S0273-0979-01-00910-7
PII:
S 0273-0979(01)00910-7
Posted:
February 7, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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