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A Remark on Partial Resolutions of 3-Dimensional Terminal Singularities

Published online by Cambridge University Press:  11 January 2016

Takayuki Hayakawa
Takayuki Hayakawa*
Affiliation:
Department of Mathematics, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192, Japan, thaya@kenroku.kanazawa-u.ac.jp
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Abstract

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Let X be a 3-dimensional terminal singularity of index ≥ 2. We study projective birational morphisms ϕ: Y → X such that the exceptional divisor of ϕ consists of all prime divisors with discrepancies < 1 (resp. ≤ 1) over X.

Keywords

14B05
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 178 , 2005 , pp. 117 - 127
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

[Alex94] Alexeev, V., General elephants of q-Fano 3-folds, Compositio Math., 91 (1994), 91–116.Google Scholar
[Art68] Artin, M., On the solutions of analytic equations, Invent. Math., 5 (1968), 277–291.CrossRefGoogle Scholar
[Art69] Artin, M., Algebraic approximation of structures over complete local rings, Publ. Math. I.H.E.S., 36 (1969), 23–58.CrossRefGoogle Scholar
[Hay99] Hayakawa, T., Blowing ups of 3-dimensional terminal singularities, Publ. RIMS, Kyoto Univ., 35 (1999), 515–570.CrossRefGoogle Scholar
[Hay00] Hayakawa, T., Blowing ups of 3-dimensional terminal singularities, II, Publ. RIMS, Kyoto Univ., 36 (2000), 423–456.CrossRefGoogle Scholar
[Hay05] Hayakawa, T., Gorenstein resolutions of 3-dimensional terminal singularities, Nagoya Math. J., 178 (2005), 63–115.CrossRefGoogle Scholar
[Kaw84] Kawamata, Y., The cone of curves of algebraic varieties, Ann. of Math., 119 (1984), 603–633.CrossRefGoogle Scholar
[FA92] Kollár, J. et al. Flips and abundance for algebraic threefolds, Astèrisque, 211 (1992).Google Scholar
[KM98] Kollár, J. and Mori, S., Birational geometry of algebraic varieties, Cambridge University Press, 1998.CrossRefGoogle Scholar
[Reid80] Reid, M., Canonical threefolds, Géométrie Algébrique Angers (A. Beauville, ed.), Sijthoff & Noordhoff (1980), pp. 273–310.Google Scholar
[Reid83] Reid, M., Minimal models of canonical threefolds, Algebraic Varieties and An alytic Varieties, Adv. Stud. Pure Math. 1, Kinokuniya and North-Holland (1983), pp. 131–180.CrossRefGoogle Scholar
[Reid87] Reid, M., Young person’s guide to canonical singularities, Algebraic Geometry, Bowdoin 1985, Proc. Symp. Pure Math., 46 (1987), pp. 345–416.Google Scholar