Letters of a Bi-rationalist. VII Ordered termination

By V. Shokurov. 2006

50 citations recorded by the source corpus.

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 termination of terminal log flips in dimension d imply, for any log pair of dimension d, the existence of a resulting model: a strictly log minimal model or a strictly log terminal Mori log fibration, and imply the existence of log flips in dimension d + 1. As a consequence, we prove the existence of a resulting model of 4-fold log pairs, the existence of log flips in dimension 5, and Geography of log models in dimension 4.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8f72b45026bf4dc7e2921f1357f0eeeb798ebfe0

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In Computational Theory and Mathematics

1. C. Birkar
2. Christopher D. Hacon
3. J. McKernan
4. J. Demailly
5. R. Svaldi
6. Hong R. Zong
7. Mihai Paun
8. Morgan V. Brown

In Geometry and Topology

1. C. Birkar
2. Christopher D. Hacon
3. J. Demailly
4. J. McKernan
5. Mihai Paun
6. Chi Li
7. O. Fujino
8. R. Svaldi

Citations in the corpus

• Extension theorems, non-vanishing and the existence of good minimal models (2010, methodology): “The existence of minimal models for klt 4-folds is proven in [Shokurov09].”
• A geometric characterization of toric varieties (2016, result): “CHARACTERISATION OF TORIC VARIETIES 13 In particular if M = ±(KX +∆) then ±(KY +Γ) is nef. We will need some preliminary results, which are simple extensions of results by Shokurov, cf. Addendum 4 of [23]. Lemma 2.2.5. Let m 1,m 2,...,mk be positive real numbers and let m and r be positive integers.”
• On existence of log minimal models II (2009, methodology): “Since we need stronger statements than those stated in [12], we give detailed proofs here (see also [3]).”
• Existence of log canonical flips and a special LMMP (2011, methodology): “ions. The proof follows the general idea of deriving termination with scaling from existence of log minimal models that was EXISTENCE OF LOG CANONICAL FLIPS AND A SPECIAL LMMP 13 developed in [8] and [29]. In [8], finiteness of models is used to get termination. However, this works only in the klt ca”