Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

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, Russ. Math.Surveys 33(2)(1978) 97-154. MR 80g:14001
  • 2. V.I. Danilov: The birational geometry of toric 3-folds. Izv. Akadem. Nauk SSSR Ser. Mat 46 (1982), 971-982; English transl., Math. USSR Izv. 21 (1983), 269-280. MR 84e:14008
  • 3. P. Griffiths, J. Harris: Principles of algebraic geometry, A Wiley-Interscience Publication. John Wiley & Sons, New York, Chichester, Brisbane, Toronto, 1978. MR 80b:14001
  • 4. Branko Grunbaum: Convex polytopes, Pure and Applied Mathematics, Volume XVI, John Wiley & Sons, New York, 1967. MR 37:2085
  • 5. H. Hironaka: Resolution of singularities of an algebraic varieties over a field of characteristic xero. I, II, Annals of Math. 79 (1964), 109-203, 205-326. MR 33:7333
  • 6. G. Kempf, F. Knudsen, D. Mumford, B.Saint-Donat: Toroidal embeddings, Lecture Notes in Math., vol. 339, Springer-Verlag, Berlin, Heidelberg, 1973. MR 44:299
  • 7. T. Oda: Torus Embeddings and Applications, Tata Inst Fund. Research, Bombay, Springer-Verlag, 1978. MR 81e:14001
  • 8. T. Oda: Convex Bodies and Algebraic Geometry. An Introduction to the Theory of Toric Varieties, Springer-Verlag, 1988. MR 88m:14038
  • 9. M. Reid: Decompositions of toric morphisms, Arithmetic and Geometry, II. Progress in Math. 36 (1983), 395-418. MR 85e:14071
  • 10. M. Teicher: On toroidal embeddings of 3-folds, Isr. J. Math 57 (1987), 46-67. MR 88m:14008

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 14E05, 14L32

Retrieve articles in all journals with MSC (1991): 14E05, 14L32

Additional Information

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

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

American Mathematical Society