We describe three-dimensional terminal toric flips. We obtain the complete local description of three-dimensional terminal toric flips.
@article{bwmeta1.element.doi-10_2478_s11533-008-0062-4,
author = {Osamu Fujino and Hiroshi Sato and Yukishige Takano and Hokuto Uehara},
title = {Three-dimensional terminal toric flips},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {46-53},
zbl = {1174.14043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0062-4}
}
Osamu Fujino; Hiroshi Sato; Yukishige Takano; Hokuto Uehara. Three-dimensional terminal toric flips. Open Mathematics, Tome 7 (2009) pp. 46-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0062-4/
[1] Fujino O., Equivariant completions of toric contraction morphisms, Tohoku Math. J., 2006, 58, 303–321 http://dx.doi.org/10.2748/tmj/1163775132[Crossref] | Zbl 1127.14047
[2] Fujino O., Special termination and reduction to pl flips, In: Flips for 3-folds and 4-folds, Oxford University Press, 2007, 63–75 | Zbl 1286.14025
[3] Fujino O., Sato H., Introduction to the toric Mori theory, Michigan Math. J., 2004, 52(3), 649–665 http://dx.doi.org/10.1307/mmj/1100623418[Crossref] | Zbl 1078.14019
[4] Fulton W., Introduction to toric varieties, Annals of Mathematics Studies 131, The William H. Roever Lectures in Geometry, Princeton University Press, Princeton, NJ, 1993 | Zbl 0813.14039
[5] Ishida M., On the terminal toric singularities of dimension three, In: Goto S. (Ed.), Commutative Algebra, Karuizawa, Japan, 1982, 54–70
[6] Ishida M., Iwashita N., Canonical cyclic quotient singularities of dimension three, Complex analytic singularities, 135–151, Adv. Stud. Pure Math., 8, North-Holland, Amsterdam, 1987 | Zbl 0627.14002
[7] Kawamata Y., Matsuda K., Matsuki K., Introduction to the minimal model problem, Algebraic geometry, Sendai, 1985, 283–360, Adv. Stud. Pure Math., 10, North-Holland, Amsterdam, 1987
[8] Matsuki K., Introduction to the Mori program, Universitext, Springer-Verlag, New York, 2002 | Zbl 0988.14007
[9] Oda T., Convex bodies and algebraic geometry, An introduction to the theory of toric varieties, Translated from the Japanese, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 15, Springer-Verlag, Berlin, 1988 | Zbl 0628.52002
[10] Reid M., Decomposition of toric morphisms, Arithmetic and geometry II, 395–418, Progr. Math., 36, Birkhäuser Boston, Boston, MA, 1983
[11] Reid M., Young person’s guide to canonical singularities, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), 345–414, Proc. Sympos. Pure Math., 46, Part 1, Amer. Math. Soc., Providence, RI, 1987
[12] Sato H., Combinatorial descriptions of toric extremal contractions, Nagoya Math. J., 2005, 180, 111–120 | Zbl 1094.14037
[13] Takano Y., On flipping contractions of three-dimensional toric varieties with non-ℚ-factorial terminal singularities, Master’s thesis, Tokyo Metropolitan University, 2008 (in Japanese)