Flip theorem and the existence of minimal models for 3-folds

@article{Mori1988FlipTA,
  title={Flip theorem and the existence of minimal models for 3-folds},
  author={Shigefumi Mori},
  journal={Journal of the American Mathematical Society},
  year={1988},
  volume={1},
  pages={117-253}
}
  • S. Mori
  • Published 1988
  • Mathematics
  • Journal of the American Mathematical Society
§ O. Introduction § I. Preliminaries and basic definitions § la (Appendix la). Results on 3-fold terminal singularities § Ib (Appendix Ib). Deformation of extremal nbds § 2. Numerical invariants ip(n), wp(O), and w;(n) § 3. Embedding dimension of (en, pn) § 4. Classification of X ::> e at P into cases § 5. Numerical calculations for (IA), (IC), (IA v) , and (IC v) § 6. Possible singularities on an extremal nbd X::> e === Wi § 7. Existence of "good" anti(bi)canonical divisor (easy case) § 8. J… Expand
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References

SHOWING 1-10 OF 48 REFERENCES
The Chern Classes and Kodaira Dimension of a Minimal Variety
This paper deals with a sort of inequality for the first and second Chern classes of normal projective varieties with numerically effective canonical classes (Theorem 1.1); to some extent it is aExpand
Terminal quotient singularities in dimensions three and four
We classify isolated terminal cyclic quotient singularities in dimension three, and isolated Gorenstein terminal cyclic quotient singularities in dimension four. In addition, we give a new proof of aExpand
Toward a numerical theory of ampleness
Introduction Chapter I. Intersection Numbers ? 1. The polynomial theorem of Snapper ? 2. The definition and some properties of intersection numbers ? 3. Degrees and Hilbert polynomials ? 4.Expand
Decomposition of Toric Morphisms
(0.1) This paper applies the ideas of Mori theory [4] to toric varieties. Let X be a projective tonic variety (over any field) constructed from a simplicial fan F. The cone of effective 1-cyclesExpand
RATIONAL SURFACES OVER PERFECT FIELDS. II
Letk be a perfect field of arbitrary characteristic. The main object of this paper is to establish some new objects associated with algebraic surfaces F defined overk which are invariants forExpand
Degeneration of surfaces with trivial canonical bundle
The object of this note is to prove the theorem stated below. The main idea of the proof, and much of the detail, are already to be found in V. I. Kulikov's important paper [K]. Our contribution toExpand
A numerical criterion for uniruledness
An n-dimensional variety X over an algebraically closed field k is said to be uniruled if there exist an (n 1)-dimensional k-variety W and a dominant rational map f: P' x W -* X. X is calledExpand
Degenerations of k3 Surfaces and Enriques Surfaces
In this paper we study good (semistable) degenerations of K3 surfaces (m = 1) and Enriques surfaces (m = 2). We obtain a classification of such degenerations under the condition that the m-canonicalExpand
On $3$-dimensional terminal singularities
Canonical and terminal singularities are introduced by M. Reid [5], [6]. He proved that 3-dimensional terminal singularities are cyclic quotient of smooth points or cDV points [6].
Algebraic approximation of structures over complete local rings
© Publications mathématiques de l’I.H.É.S., 1969, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://Expand
...
1
2
3
4
5
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