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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Decomposition of Birational Toric Maps in Blow-Ups and Blow-Downs

Author: Jaroslaw Wlodarczyk
Journal: Trans. Amer. Math. Soc. 349 (1997), 373-411
MSC (1991): Primary 14E05; Secondary 14L32
MathSciNet review: 1370654
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that a toric birational map between two complete
smooth toric varieties of the same dimension can be decomposed in a sequence of equivariant blow-ups and blow-downs along smooth centers.

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

  • 1. V. I. Danilov, The geometry of toric varieties, Uspekhi Mat. Nauk 33 (1978), no. 2(200), 85–134, 247 (Russian). MR 495499 (80g:14001)
  • 2. V. I. Danilov, Birational geometry of three-dimensional toric varieties, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 5, 971–982, 1135 (Russian). MR 675526 (84e:14008)
  • 3. Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Wiley-Interscience [John Wiley & Sons], New York, 1978. Pure and Applied Mathematics. MR 507725 (80b:14001)
  • 4. Branko Grünbaum, Convex polytopes, With the cooperation of Victor Klee, M. A. Perles and G. C. Shephard. Pure and Applied Mathematics, Vol. 16, Interscience Publishers John Wiley & Sons, Inc., New York, 1967. MR 0226496 (37 #2085)
  • 5. 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 (33 #7333)
  • 6. G. N. Nilov, The number of subgroups of order three of the symmetric group, Kabardino-Balkarsk. Gos. Univ. Učen. Zap. No. 3 (1959), 215–216 (Russian). MR 0283066 (44 #299)
  • 7. Tadao Oda, Torus embeddings and applications, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 57, Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin-New York, 1978. Based on joint work with Katsuya Miyake. MR 546291 (81e:14001)
  • 8. Tadao Oda, Convex bodies and algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 15, Springer-Verlag, Berlin, 1988. An introduction to the theory of toric varieties; Translated from the Japanese. MR 922894 (88m:14038)
  • 9. Miles Reid, Decomposition of toric morphisms, Arithmetic and geometry, Vol. II, Progr. Math., vol. 36, Birkhäuser Boston, Boston, MA, 1983, pp. 395–418. MR 717617 (85e:14071)
  • 10. Mina Teicher, On toroidal embeddings of 3-folds, Israel J. Math. 57 (1987), no. 1, 49–67. MR 882246 (88m:14008),

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Additional Information

Jaroslaw Wlodarczyk
Affiliation: Institute of Matematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland

PII: S 0002-9947(97)01701-7
Received by editor(s): March 9, 1994
Received by editor(s) in revised form: December 15, 1995
Additional Notes: This work was partially supported by Deutsche Forschungsgemeischaft and KBN
Article copyright: © Copyright 1997 American Mathematical Society

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