Explicit resolution of three dimensional terminal singularities

We prove that any three dimensional terminal singularity $P \in X$ can be resolved by a sequence of divisorial contractions with minimal discrepancies which are weighted blowups over points.

[1]  M. Kawakita.  Supplement to classification of three-fold divisorial contractions , 2011, 1103.1182.

[2]  A. Koll.  Real Algebraic Threefolds Ii. Minimal Model Program , 2007 .

[3]  M. Kawakita.  Three-fold divisorial contractions to singularities of higher indices , 2003, math/0306065.

[4]  早川 貴之.  Blowing ups of 3-dimensional terminal singularities , 2003 .

[5]  M. Kawakita.  Divisorial contractions in dimension three which contract divisors to smooth points , 2000, math/0005207.

[6]  Takayuki Hayakawa.  Blowing Ups of 3-dimensional Terminal singularities, II , 2000 .

[7]  J. Kollár.  Real algebraic threefolds II. Minimal model program , 1997, alg-geom/9712005.

[8]  Y. Kawamata.  Divisorial contractions to 3-dimensional terminal quotient singularities , 1996 .

[9]  D. Markushevich.  Minimal Discrepancy for a Terminal cDV Singularity Is 1 , 1996 .

[10]  J. Kollár,et al.  Classification of three-dimensional flips , 1992 .

[11]  János Kollár.  Flops , 1989, Nagoya Mathematical Journal.

[12]  J. Kollár,et al.  Threefolds and deformations of surface singularities , 1988 .

[13]  S. D. Cutkosky,et al.  Elementary contractions of Gorenstein threefolds , 1988 .

[14]  Shigefumi Mori,et al.  Flip theorem and the existence of minimal models for 3-folds , 1988 .

[15]  V. Shokurov,et al.  THE NONVANISHING THEOREM , 1986 .

[16]  S. Mori.  On 3-dimensional terminal singularities , 1985, Nagoya Mathematical Journal.

[17]  Miles Reid,et al.  Young person''s guide to canonical singularities , 1985 .

[18]  M. Reid.  Minimal Models of Canonical 3-Folds , 1983 .

[19]  S. Mori.  Threefolds whose canonical bundles are not numerically effective. , 1980, Proceedings of the National Academy of Sciences of the United States of America.

[20]  D. Gorenstein,et al.  Algebraic approximation of structures over complete local rings , 1969 .