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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: János Kollár
Title: Rational curves on algebraic varieties
Additional book information: Springer, Secaucus, NJ, 1996, viii+320 pp., ISBN 3-540-60168-6, $139.95$

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

M. Artin, Deformations of singularities, Tata Inst. lecture notes 54, 1976
A. Corti and M. Reid (eds.), Explicit birational geometry of 3-folds, CUP 2000, ISBN 0 521 63641 8
A. Grothendieck, Techniques de construction et théorèmes d'existence en géométrie algébrique. IV. Les schémas de Hilbert, Sém. Bourbaki 6 Exp. 221, 249-276, Soc. Math. France, 1995 CMP 98:09
János Kollár, The structure of algebraic threefolds: an introduction to Mori's program, Bull. Amer. Math. Soc. (N.S.) 17 (1987) 211-273 MR 0903730
János Kollár, Yoichi Miyaoka and Shigefumi Mori, Rational connectedness and boundedness of Fano manifolds, J. Diff. Geom. 36 (1992) 765-779 MR 1189503
Y. Miyaoka, Rational curves on algebraic varieties, in Proc. Internat. Congress of Math (Zürich, 1994), Birkhäuser, Basel, 1995. pp. 680-689MR 1403968
Yoichi Miyaoka and Shigefumi Mori, A numerical criterion for uniruledness, Ann. of Math. 124 (1986) 65-69 MR 0847952
S. Mori, Projective manifolds with ample tangent bundles, Ann. of Math. (2) 110 (1979) 593-606 MR 0554387
S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982) 133-176 MR 0662120
D. Mumford, Lectures on curves on an algebraic surface, Princeton University Press, 1966MR 0209285
M. Reid, Infinitesimal view of extending a hyperplane section - deformation theory and computer algebra, in Algebraic geometry (L'Aquila, 1988), Springer LNM 1417, 1990, pp. 214-286 MR 1040562
Edoardo Sernesi, Topics on families of projective schemes, Queen's papers in pure and appl. math 73 (1986), viii+203 pp.MR 0869062

Review Information:

Reviewer: Miles Reid
Affiliation: Math Institute, University of Warwick
Journal: Bull. Amer. Math. Soc. 38 (2001), 109-115
Published electronically: October 2, 2000
Review copyright: © Copyright 2000 American Mathematical Society