an:00699551
Zbl 0860.14016
Shokurov, V. V.
Semistable 3-fold flips
EN
Russ. Acad. Sci., Izv., Math. 42, No. 2, 371-425 (1994); reprint from Izv. Ross. Akad. Nauk, Ser. Mat. 57, No. 2, 165-222 (1993).
1064-5632
1993
j
14E30 14J30 14E05 14E15
normal analytic threefold; terminal singularities; semistable divisor; minimal semistable model; Brieskorn-Tjurina simultaneous resolution
The author gives a notion of semistability generalizing the similar one for a semistable surface degeneration.
On a normal analytic 3-fold \(X\) with terminal singularities, a semistable divisor is defined to be a reduced divisor \(D\), where all irreducible components are normal \(\mathbb{Q}\)-Cartier-divisors such that locally there exists a resolution \(g:Y \to X\) with a divisor \(g^*D\) having nonsingular irreducible components with normal crossings and such that \(g\) is decomposable into a product of locally projective morphisms on a sequence of 3-folds with terminal singularities, where \(D\) induces divisors having irreducible components which are normal Cartier-divisors. The singularities on \(X\) (``semistable singularities'') are described in this paper in a ``... half-inductive and half explicit'' way. This includes results on ``semistable blowing down'' and ``semistable flips''.
The applications in the final sections are devoted to more detailed studies and include the existence of a minimal semistable model. This has (among others) as a consequence the existence of the Brieskorn-Tjurina simultaneous resolution.
M.Roczen (Berlin)