Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T17:50:40.011Z Has data issue: false hasContentIssue false

A Remark on Partial Resolutions of 3-Dimensional Terminal Singularities

Published online by Cambridge University Press:  11 January 2016

Takayuki Hayakawa*
Affiliation:
Department of Mathematics, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192, Japan, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Keywords

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

[Alex94] Alexeev, V., General elephants of q-Fano 3-folds, Compositio Math., 91 (1994), 91116.Google Scholar
[Art68] Artin, M., On the solutions of analytic equations, Invent. Math., 5 (1968), 277291.CrossRefGoogle Scholar
[Art69] Artin, M., Algebraic approximation of structures over complete local rings, Publ. Math. I.H.E.S., 36 (1969), 2358.CrossRefGoogle Scholar
[Hay99] Hayakawa, T., Blowing ups of 3-dimensional terminal singularities, Publ. RIMS, Kyoto Univ., 35 (1999), 515570.CrossRefGoogle Scholar
[Hay00] Hayakawa, T., Blowing ups of 3-dimensional terminal singularities, II, Publ. RIMS, Kyoto Univ., 36 (2000), 423456.CrossRefGoogle Scholar
[Hay05] Hayakawa, T., Gorenstein resolutions of 3-dimensional terminal singularities, Nagoya Math. J., 178 (2005), 63115.CrossRefGoogle Scholar
[Kaw84] Kawamata, Y., The cone of curves of algebraic varieties, Ann. of Math., 119 (1984), 603633.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. 273310.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. 131180.CrossRefGoogle Scholar
[Reid87] Reid, M., Young person’s guide to canonical singularities, Algebraic Geometry, Bowdoin 1985, Proc. Symp. Pure Math., 46 (1987), pp. 345416.Google Scholar