Three-dimensional terminal toric flips

• Autorzy: Osamu Fujino , Hiroshi Sato , Yukishige Takano , Hokuto Uehara
• Języki publikacji: EN

Abstrakty

EN

We describe three-dimensional terminal toric flips. We obtain the complete local description of three-dimensional terminal toric flips.

Słowa kluczowe

EN

Toric variety; Mori theory; Terminal flip

Kategorie tematyczne

• 14B05: Singularities
• 14M25: Toric varieties, Newton polyhedra
• 14E30: Minimal model program (Mori theory, extremal rays)
• 14J30: 3 -folds

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 1
• Strony: 46-53

Daty

wydano

2009-03-01

online

2009-01-10

Twórcy

autor

Osamu Fujino

• Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, Japan

autor

Hiroshi Sato

• Faculty of Economics and Information, Gifu Shotoku Gakuen University, Nakauzura Gifu, Japan

autor

Yukishige Takano

• Department of Mathematics, Tokyo Metropolitan University, Tokyo, Japan

autor

Hokuto Uehara

• Department of Mathematics, Tokyo Metropolitan University, Tokyo, Japan

Bibliografia

• [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]
• [2] Fujino O., Special termination and reduction to pl flips, In: Flips for 3-folds and 4-folds, Oxford University Press, 2007, 63–75
• [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]
• [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
• [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
• [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
• [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
• [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
• [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)

Identyfikatory

DOI

10.2478/s11533-008-0062-4