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Bulletin of the American Mathematical Society

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Book Review

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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?)

  • [A] M. Artin, Deformations of singularities, Tata Inst. lecture notes 54, 1976
  • [CR] A. Corti and M. Reid (eds.), Explicit birational geometry of 3-folds, CUP 2000, ISBN 0 521 63641 8
  • [G] 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
  • [Ko] János Kollár, The structure of algebraic threefolds: an introduction to Mori's program, Bull. Amer. Math. Soc. (N.S.) 17 (1987) 211-273 MR 88i:14030
  • [KMM] János Kollár, Yoichi Miyaoka and Shigefumi Mori, Rational connectedness and boundedness of Fano manifolds, J. Diff. Geom. 36 (1992) 765-779 MR 94g:14021
  • [Mi] Y. Miyaoka, Rational curves on algebraic varieties, in Proc. Internat. Congress of Math (Zürich, 1994), Birkhäuser, Basel, 1995. pp. 680-689MR 97k:14043
  • [MM] Yoichi Miyaoka and Shigefumi Mori, A numerical criterion for uniruledness, Ann. of Math. 124 (1986) 65-69 MR 87k:14046
  • [M1] S. Mori, Projective manifolds with ample tangent bundles, Ann. of Math. (2) 110 (1979) 593-606 MR 81j:14010
  • [M2] S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982) 133-176 MR 84e:14032
  • [Mu] D. Mumford, Lectures on curves on an algebraic surface, Princeton University Press, 1966MR 35:187
  • [R] 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 91h:14018
  • [S] Edoardo Sernesi, Topics on families of projective schemes, Queen's papers in pure and appl. math 73 (1986), viii+203 pp.MR 88b:14006

Review Information:

Reviewer: Miles Reid
Affiliation: Math Institute, University of Warwick
Journal: Bull. Amer. Math. Soc. 38 (2001), 109-115
MSC (1991): Primary 14-02, 14C05, 14E30, 14J26, 14J45, 14M20, 14C40, 14E35, 14H10, 14J10
Published electronically: October 2, 2000
Review copyright: © Copyright 2000 American Mathematical Society