Corpus ID: 10864638

On the existence of flips

@article{Hacon2005OnTE,
  title={On the existence of flips},
  author={Christopher D. Hacon and James McKernan},
  journal={arXiv: Algebraic Geometry},
  year={2005}
}
We prove the existence of flips in dimension n, contingent on the termination of real flips in dimension n-1. 
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References

SHOWING 1-10 OF 25 REFERENCES
On the extension problem of pluricanonical forms
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
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 logExpand
ACC for log canonical thresholds and termination of log flips
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 flipsExpand
Invariance of plurigenera
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 manifoldsExpand
Boundedness of pluricanonical maps of varieties of general type
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 anyExpand
Minimal models and the Kodaira dimension of algebraic fiber spaces.
(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 ViehwegExpand
Flip theorem and the existence of minimal models for 3-folds
§ 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 invariantsExpand
Classical setting : line bundles and linear series
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
...
1
2
3
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