#### 22 Citations

Existence of minimal models for varieties of log general type

- Mathematics
- 2006

Assuming finite generation in dimension n − 1, we prove that pl-flips exist in dimension n.

Introduction to the Minimal Model Program and the existence of flips

- Mathematics
- 2008

The first aim of this note is to give a concise, but complete and self-contained, presentation of the fundamental theorems of Mori theory - the nonvanishing, base point free, rationality and cone… Expand

On a comparison of minimal log discrepancies in terms of motivic integration

- Mathematics
- 2006

Abstract We formulate a comparison of minimal log discrepancies of a variety and its ambient space with appropriate boundaries in terms of motivic integration. It was obtained also by Ein and Mustaţă… Expand

Restrictions of log canonical algebras of general type

- Mathematics
- 2005

We introduce a diophantine property of a log canonical algebra, and use it to describe the restriction of a log canonical algebra of general type to a log canonical center of codimension one.

Flips for 3-folds and 4-folds

- Mathematics
- 2007

1. Introduction 2. 3-fold flips after Shokurov 3. What is log terminal? 4. Special termination and reduction to pl flips 5. Extension theorems and the existence of flips 6. Saturated mobile… Expand

Exercises in the birational geometry of algebraic varieties

- Mathematics
- 2008

This a collection of about 100 exercises. It could be used as a supplement to the book Koll\'ar--Mori: Birational geometry of algebraic varieties.

Termination of (many) 4-dimensional log flips

- Mathematics
- 2007

We prove that any sequence of 4-dimensional log flips that begins with a klt pair (X,D) such that -(KX+D) is numerically equivalent to an effective divisor, terminates. This implies termination of… Expand

Extension of sections via adjoint ideals

- Mathematics
- 2008

We prove theorems on extending sections of line bundles from divisors to the ambient space, inspired by various results of Siu, Kawamata, and especially Hacon–McKernan and Takayama. We include… Expand

Letters of a Bi-rationalist. VII Ordered termination

- Mathematics
- 2006

To construct a resulting model in the LMMP, it is sufficient to prove the existence of log flips and their termination for some sequences. We prove that the LMMP in dimension d − 1 and the… Expand

On existence of log minimal models

- Mathematics
- Compositio Mathematica
- 2010

Abstract In this paper, we prove that the log minimal model program in dimension d−1 implies the existence of log minimal models for effective lc pairs (e.g. of non-negative Kodaira dimension) in… Expand

#### References

SHOWING 1-10 OF 25 REFERENCES

On the extension problem of pluricanonical forms

- Mathematics
- 1998

We review some recent development on the extension problem of pluricanonical forms from a divisor to the ambient space in [Si], [K5] and [N3] with simplified proofs.

3-FOLD LOG FLIPS

- Mathematics
- 1993

We prove that 3-fold log flips exist. We deduce the existence of log canonical and -factorial log terminal models, as well as a positive answer to the inversion problem for log canonical and log… Expand

ACC for log canonical thresholds and termination of log flips

- Mathematics
- 2005

We prove that the ascending chain condition (ACC) for log canonical (lc) thresholds in dimension $d$ and Special Termination in dimension $d$ imply the termination of any sequence of log flips… Expand

Invariance of plurigenera

- Mathematics
- 1998

In this paper we give a proof of the following long conjectured result on the invariance of the plurigenera. Main Theorem. Let p : X ! D be a smooth projective family of compact complex manifolds… Expand

Boundedness of pluricanonical maps of varieties of general type

- Mathematics
- 2006

Using the techniques of [20] and [10], we prove that certain log forms may be lifted from a divisor to the ambient variety. As a consequence of this result, following [22], we show that: For any… Expand

Minimal models and the Kodaira dimension of algebraic fiber spaces.

- Mathematics
- 1985

(litaka [21]). In 1977, the first affirmative answer to this conjecture in the case where dimX = dimS + l was given by E. Viehweg [47] by extending the method of Ueno [44]. From this result Viehweg… Expand

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

- Mathematics
- 1988

§ 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… Expand

Classical setting : line bundles and linear series

- Mathematics
- 2004

Notation and Conventions.- One: Ample Line Bundles and Linear Series.- to Part One.- 1 Ample and Nef Line Bundles.- 2 Linear Series.- 3 Geometric Manifestations of Positivity.- 4 Vanishing Theorems.-… Expand

Shokurov, 3–fold log flips

- Russian Acad. Sci. Izv. Math
- 1993