Book Review

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Book Information:

Editors: H. Hauser, J. Lipman, F. Oort and A. Quirós (eds.)

Title: Alterations and resolution of singularities

Additional book information: edited by H. Hauser, J. Lipman, F. Oort and A. Quirós (eds.), Birkhäuser, Basel, 2000, xxi+598 pp., ISBN 3-7643-6178-6, $108.00

**1.**G. V. Belyĭ,*Galois extensions of a maximal cyclotomic field*, Izv. Akad. Nauk SSSR Ser. Mat.**43**(1979), no. 2, 267–276, 479 (Russian). MR**534593****2.**Edward Bierstone and Pierre D. Milman,*Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant*, Invent. Math.**128**(1997), no. 2, 207–302. MR**1440306**, https://doi.org/10.1007/s002220050141**3.**Heisuke Hironaka,*Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II*, Ann. of Math. (2) 79 (1964), 109–203; ibid. (2)**79**(1964), 205–326. MR**0199184****4.**János Kollár and Shigefumi Mori,*Birational geometry of algebraic varieties*, Cambridge Tracts in Mathematics, vol. 134, Cambridge University Press, Cambridge, 1998. With the collaboration of C. H. Clemens and A. Corti; Translated from the 1998 Japanese original. MR**1658959****5.**Mark Spivakovsky,*A solution to Hironaka’s polyhedra game*, Arithmetic and geometry, Vol. II, Progr. Math., vol. 36, Birkhäuser Boston, Boston, MA, 1983, pp. 419–432. MR**717618****6.**Oscar Zariski,*Collected papers. Vol. I: Foundations of algebraic geometry and resolution of singularities*, The MIT Press, Cambridge, Mass.-London, 1972. Edited by H. Hironaka and D. Mumford; Mathematicians of Our Time, Vol. 2. MR**0505100**

Oscar Zariski,*Collected papers. Vol. II: Holomorphic functions and linear systems*, The MIT Press, Cambridge, Mass.-London, 1973. Edited by M. Artin and D. Mumford; Mathematicians of Our Time, Vol. 6. MR**0505101**

Oscar Zariski,*Collected papers. Vol. III*, The MIT Press, Cambridge, Mass.-London, 1978. Topology of curves and surfaces, and special topics in the theory of algebraic varieties; Edited and with an introduction by M. Artin and B. Mazur; Mathematicians of Our Time. MR**0505104**

Oscar Zariski,*Collected papers. Vol. I: Foundations of algebraic geometry and resolution of singularities*, The MIT Press, Cambridge, Mass.-London, 1972. Edited by H. Hironaka and D. Mumford; Mathematicians of Our Time, Vol. 2. MR**0505100**

Oscar Zariski,*Collected papers. Vol. II: Holomorphic functions and linear systems*, The MIT Press, Cambridge, Mass.-London, 1973. Edited by M. Artin and D. Mumford; Mathematicians of Our Time, Vol. 6. MR**0505101**

Oscar Zariski,*Collected papers. Vol. III*, The MIT Press, Cambridge, Mass.-London, 1978. Topology of curves and surfaces, and special topics in the theory of algebraic varieties; Edited and with an introduction by M. Artin and B. Mazur; Mathematicians of Our Time. MR**0505104**

Oscar Zariski,*Collected papers. Vol. I: Foundations of algebraic geometry and resolution of singularities*, The MIT Press, Cambridge, Mass.-London, 1972. Edited by H. Hironaka and D. Mumford; Mathematicians of Our Time, Vol. 2. MR**0505100**

Oscar Zariski,*Collected papers. Vol. II: Holomorphic functions and linear systems*, The MIT Press, Cambridge, Mass.-London, 1973. Edited by M. Artin and D. Mumford; Mathematicians of Our Time, Vol. 6. MR**0505101**

Oscar Zariski,*Collected papers. Vol. III*, The MIT Press, Cambridge, Mass.-London, 1978. Topology of curves and surfaces, and special topics in the theory of algebraic varieties; Edited and with an introduction by M. Artin and B. Mazur; Mathematicians of Our Time. MR**0505104**

Oscar Zariski,*Collected papers. Vol. IV*, Mathematicians of Our Time, vol. 16, MIT Press, Cambridge, Mass.-London, 1979. Equisingularity on algebraic varieties; Edited and with an introduction by J. Lipman and B. Teissier. MR**545653**

Review Information:

Reviewer: Fedor Bogomolov

Affiliation: Courant Institute, NYU

Email: bogomolo@cims.nyu.edu

Reviewer: Yuri Tschinkel

Affiliation: University of Illinois at Chicago

Email: yuri@math.uic.edu

Journal: Bull. Amer. Math. Soc.

**39**(2002), 95-100

Published electronically: October 10, 2001

Review copyright: © Copyright 2001 American Mathematical Society