Nagoya Mathematical Journal

A remark on partial resolutions of $3$-dimensional terminal singularities

Takayuki Hayakawa
Source: Nagoya Math. J. Volume 178 (2005), 117-127.

Abstract

Let $X$ be a $3$-dimensional terminal singularity of index $\geq 2$. We study projective birational morphisms $\varphi : Y \to X$ such that the exceptional divisor of $\varphi$ consists of all prime divisors with discrepancies $< 1$ (resp.\ $\leq 1$) over $X$.

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Primary Subjects: 14B05
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.nmj/1124217073
Mathematical Reviews number (MathSciNet): MR2145317
Zentralblatt MATH identifier: 1081.14004

References

V. Alexeev, General elephants of $\Bbb Q$-Fano $3$-folds , Compositio Math., 91 (1994), 91--116.
Mathematical Reviews (MathSciNet): MR1273928
M. Artin, On the solutions of analytic equations , Invent. Math., 5 (1968), 277--291.
Mathematical Reviews (MathSciNet): MR232018
Digital Object Identifier: doi:10.1007/BF01389777
--------, Algebraic approximation of structures over complete local rings , Publ. Math. I.H.E.S., 36 (1969), 23--58.
Mathematical Reviews (MathSciNet): MR268188
T. Hayakawa, Blowing ups of $3$-dimensional terminal singularities , Publ. RIMS, Kyoto Univ., 35 (1999), 515--570.
Mathematical Reviews (MathSciNet): MR1710753
--------, Blowing ups of $3$-dimensional terminal singularities, II , Publ. RIMS, Kyoto Univ., 36 (2000), 423--456.
Mathematical Reviews (MathSciNet): MR1781436
--------, Gorenstein resolutions of $3$-dimensional terminal singularities , Nagoya Math. J., 178 (2005), 63--115.
Mathematical Reviews (MathSciNet): MR2145316
Y. Kawamata, The cone of curves of algebraic varieties , Ann. of Math., 119 (1984), 603--633.
Mathematical Reviews (MathSciNet): MR744865
Digital Object Identifier: doi:10.2307/2007087
J. Kollár et al., Flips and abundance for algebraic threefolds , Astérisque, 211 (1992).
J. Kollár and S. Mori, Birational geometry of algebraic varieties, Cambridge University Press (1998).
Mathematical Reviews (MathSciNet): MR1658959
M. Reid, Canonical threefolds , Géométrie Algébrique Angers (A. Beauville, ed.), Sijthoff & Noordhoff (1980), 273--310.
--------, Minimal models of canonical threefolds , Algebraic Varieties and Analytic Varieties, Adv. Stud. Pure Math. 1, Kinokuniya and North-Holland (1983), 131--180.
--------, Young person's guide to canonical singularities , Algebraic Geometry, Bowdoin 1985, Proc. Symp. Pure Math., 46 (1987), 345--416.
Zentralblatt MATH: 0634.14003

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Nagoya Mathematical Journal

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