On semistable Mori contractions
Izvestiya. Mathematics , Tome 68 (2004) no. 2, pp. 365-374.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study Fano–Mori contractions with fibres of dimension at most one satisfying the semistability assumption. In particular, we give a new proof of the existence of semistable 3-fold flips.
@article{IM2_2004_68_2_a6,
     author = {Yu. G. Prokhorov},
     title = {On semistable {Mori} contractions},
     journal = {Izvestiya. Mathematics },
     pages = {365--374},
     publisher = {mathdoc},
     volume = {68},
     number = {2},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2004_68_2_a6/}
}
TY  - JOUR
AU  - Yu. G. Prokhorov
TI  - On semistable Mori contractions
JO  - Izvestiya. Mathematics 
PY  - 2004
SP  - 365
EP  - 374
VL  - 68
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2004_68_2_a6/
LA  - en
ID  - IM2_2004_68_2_a6
ER  - 
%0 Journal Article
%A Yu. G. Prokhorov
%T On semistable Mori contractions
%J Izvestiya. Mathematics 
%D 2004
%P 365-374
%V 68
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2004_68_2_a6/
%G en
%F IM2_2004_68_2_a6
Yu. G. Prokhorov. On semistable Mori contractions. Izvestiya. Mathematics , Tome 68 (2004) no. 2, pp. 365-374. http://geodesic.mathdoc.fr/item/IM2_2004_68_2_a6/

[1] Corti A., Semistable $3$-fold flips, E-print alg-geom/9505035

[2] Looijenga E., Wahl J., “Quadratic functions and smoothing surface singularities”, Topology, 25 (1986), 261–291 | DOI | MR | Zbl

[3] Mori S., “Flip theorem and the existence of minimal models for $3$-folds”, J. Amer. Math. Soc., 1 (1988), 117–253 | DOI | MR | Zbl

[4] Kawamata Y., “Crepant blowing-up of $3$-dimensional canonical singularities and its application to degenerations of surfaces”, Ann. Math. (2), 127 (1988), 93–163 | DOI | MR | Zbl

[5] Kawamata Y., “Semistable minimal models of threefolds in positive or mixed characteristic”, J. Alg. Geom., 3 (1994), 463–491 | MR | Zbl

[6] Kollár J., “Flops”, Nagoya Math. J., 113 (1989), 15–36 | MR | Zbl

[7] Kollár J., Mori S., “Classification of three-dimensional flips”, J. Amer. Math. Soc., 5 (1992), 533–703 | DOI | MR | Zbl

[8] Kollár J., Mori S., “Birational geometry of algebraic varieties”, Cambridge Tracts in Mathematics, 134, Cambridge Univ. Press, Cambridge, 1998 | MR | Zbl

[9] Kollár J., Shepherd-Barron N. I., “Threefolds and deformations of surface singularities”, Invent. Math., 91 (1988), 299–338 | DOI | MR | Zbl

[10] Kollár J. et al., “Flips and abundance for algebraic threefolds”, A summer seminar at the Univ. of Utah (Salt Lake City, 1991), Astérisque, 211, 1992 | MR

[11] Kulikov Vik. S., “Vyrozhdeniya K3-poverkhnostei i poverkhnostei Enrikvesa”, Izv. AN SSSR. Ser. matem., 41:5 (1977), 1008–1042 | MR | Zbl

[12] Prokhorov Yu. G., Lectures on complements on log surfaces, MSJ Memoirs, 10, Mathematical Society of Japan, Tokyo, 2001 | MR

[13] Prokhorov Yu. G., Shokurov V. V., “Pervaya osnovnaya teorema o dopolneniyakh: ot lokalnogo k globalnomu”, Izv. RAN. Ser. matem., 65:6 (2001), 99–128 | MR | Zbl

[14] Shokurov V. V., “Trekhmernye logperestroiki”, Izv. RAN. Ser. matem., 56:1 (1992), 105–203 | MR | Zbl

[15] Shokurov V. V., “Semistable $3$-fold flips”, Izv. RAN. Ser. matem., 57:2 (1993), 165–224 | MR

[16] Tsunoda Sh., “Degenerations of surfaces”, Algebraic geometry (Sendai, 1985), Adv. Stud. Pure Math., 10, North-Holland, Amsterdam, 1987, 755–764 | MR