Families of D-minimal Models and Applications to 3-fold Divisorial Contractions
نویسنده
چکیده
Let X/T be a one parameter family of canonical 3-folds and let D be a Weil divisor on it flat over T . We study the problem of when the Dt-minimal models of Xt form a family and we obtain conditions for this to happen. As an application of this we classify terminal divisorial contractions E ⊂ Y −→ Γ ⊂ X contracting an irreducible surface E onto the smooth curve Γ, in the case when the general section of X through Γ is a D5 DuVal singularity.
منابع مشابه
SIMULTANEOUS Q-FACTORIALIZATION OF DIVISORS AND APPLICATIONS TO 3-FOLD DIVISORIAL CONTRACTIONS THAT CONTRACT A DIVISOR ONTO A CURVE THROUGH A cD5 SINGULARITY
Let Γ ⊂ X be a smooth curve on a 3-fold. In this paper we classify terminal divisorial contractions E ⊂ Y −→ Γ ⊂ X contracting an irreducible surface E onto Γ, in the case when the general section of X containing Γ has D5 type singularities. In doing so we consider the problem of existence of MMP in families of canonical 3-folds, and we get results about existence of simultaneous Q-factorialisa...
متن کاملDivisorial Contractions to Some Gorenstein Singularities
Divisorial contractions to singularities, defined by equations xy + zn + un = 0 n ≥ 3 and xy + z + u = 0 are classified. The problem of birational classification of algebraic varieties is highly interconnected with the problem of description of singularities on them. One of the most important class of three-dimensional singularities is terminal singularities, which arise within minimal models p...
متن کامل3-FOLD DIVISORIAL CONTRACTIONS OF DIVISORS TO CURVES THROUGH cE7 COMPOUND DUVAL SINGULARITIES
In this paper we present a complete classification of 3-fold divisorial contractions E ⊂ Y f −→ X ⊃ Γ where Γ is a smooth curve, X is Gorenstein and the general hyperplane section of X containing Γ is DuVal of type E6.
متن کاملTerminal 3-fold Divisorial Contractions of a Surface to a Curve I
Let Γ ⊂ X be a smooth curve on a 3-fold which has only index 1 terminal singularities along this curve. In this paper we investigate the existence of extremal terminal divisorial contractions E ⊂ Y −→ Γ ⊂ X , contracting an irreducible surface E to Γ. We consider cases with respect to the singularities of the general hypersurface section S of X through Γ. We completely classify the cases when S...
متن کاملOn the Fourth Adjoint Contractions of Divisorial and Fiber Types
In this paper, we will list up all the cases for the ray contractions of divisorial and fiber types for smooth projective varieties of dimension five. These are obtained as a corollary from the lists of n-dimensional k-th adjoint contractions f : X → Y of the same types for k = 1, 2, 3 and 4 (n ≥ 5). The lists for k = 1, 2 and 3 have previously been obtained in [Na, Proposition 1.2 and Theorem ...
متن کامل