On semistable Mori contractions

Prokhorov, Yuri

doi:10.1070/im2004v068n02abeh000478

Cited by 4 publications

(5 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The latter existence result can readily be established according to the existence of 1-complements in the sense of the second author (see [34], § 5, [21], § 19). New constructions and generalizations of semistable flips are being published [29] up to the present time. All these constructions and proofs make essential use of the classification of lc singularities in dimension 2.…”

Section: S(b)mentioning

confidence: 99%

“…(ii) The stable Q-factorial property of moderate singularities is an innovation introduced by Corti in [5], where a generalization of Theorem 7.4 to a broader class of singularities is also given (cf. Corti's somewhat free definition of semistable singularities in [5], 2.5; in the Russian terminology, these singularities are said to be q-semistable [29]).…”

Section: S(b)mentioning

confidence: 99%

See 1 more Smart Citation

Birational models and flips

Iskovskikh¹,

Shokurov²

2005

Russ. Math. Surv.

View full text Add to dashboard Cite

This survey treats two chapters in the theory of log minimal models, namely, the chapter on different notions of models in this theory and the chapter on birational flips, that is, log flips, mainly in dimension 3. Our treatment is based on ideas and results of the second author: his paper on log flips (and also on material from the University of Utah workshop) for the first chapter, and his paper on prelimiting flips (together with surveys of these results by Corti and Iskovskikh) for the second chapter, where a complete proof of the existence of log flips in dimension 3 is given. At present, this proof is the simplest one, and the authors hope that it can be understood by a broad circle of mathematicians. Contents Der Vogelsprecher bin ich ja, Stets lustig heißa hopsassa ! Ich Vogelsprecher bin bekannt bei Alt und Jung im ganzen Land. Weiß mit dem Locken umzugehn und mich aufs Pfeifen zu verstehn !

show abstract

Section: S(b)mentioning

confidence: 99%

Section: S(b)mentioning

confidence: 99%

Birational models and flips

Iskovskikh¹,

Shokurov²

2005

Russ. Math. Surv.

View full text Add to dashboard Cite

show abstract

“…In this section, we construct examples of T-conic bundles. The same approach was used in [8] in the proof of the existence of 1-complements. Notation 5.1.…”

Section: Examplesmentioning

confidence: 99%

“…In this paper, we propose a method of construction of examples of Mori contractions from threefolds to surfaces (see [6][7][8]). We refer the reader to [3,5] for the terminology of the minimal model theory.…”

Section: Introductionmentioning

confidence: 99%

On Semistable Mori Conic Bundles

Prokhorov

2005

J Math Sci

View full text Add to dashboard Cite

show abstract

“…Thus at the moment the less investigated case is the case where the base is smooth and the central fiber C is reducible. This class of Q-conic bundles was studied only under additional assumption of "semistability" [Pro04], [Pro05].…”

Section: Theorem 13 (Cf [Km92 (22)])mentioning

confidence: 99%

On $ℚ$-Conic Bundles, III

Nagata¹,

Mori²,

Prokhorov³

2009

Publ. Res. Inst. Math. Sci.

View full text Add to dashboard Cite

A Q-conic bundle germ is a proper morphism from a threefold with only terminal singularities to the germ (Z o) of a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. Building upon our previous paper [MP08a], we prove the existence of a Du Val anti-canonical member under the assumption that the central fiber is irreducible. §1. IntroductionThe present paper is a continuation of a series of papers [MP08a], [MP08b]. Recall that a Q-conic bundle is a projective morphism f : X → Z from an (algebraic or analytic) threefold with terminal singularities to a surface that satisfies the following properties:For f : X → Z as above and for a point o ∈ Z, we call the analytic germ (X, f −1 (o) red ) a Q-conic bundle germ.In this paper we complete the proof of the following

show abstract

On semistable Mori contractions

Abstract: Abstract. We study Fano-Mori contractions with fibers of dimension at most one satisfying the semistability assumption. As an application of our technique we give a new proof of the existence of semistable 3-fold flips.

Cited by 4 publications

References 17 publications

Birational models and flips

Birational models and flips

On Semistable Mori Conic Bundles

On $ℚ$-Conic Bundles, III

Contact Info

Product

Resources

About