Existence of log canonical flips and a special LMMP
By C. Birkar. Publications mathématiques (Bures-sur-Yvette), 2011
181 citations recorded by the source corpus.
Let (X/Z,B+A) be a Q-factorial dlt pair where B,A≥0 are Q-divisors and KX+B+A∼Q0/Z. We prove that any LMMP/Z on KX+B with scaling of an ample/Z divisor terminates with a good log minimal model or a Mori fibre space. We show that a more general statement follows from the ACC for lc thresholds. An immediate corollary of these results is that log flips exist for log canonical pairs.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e5b9d31507a09e56a22a0e3c0fb994904be182df
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In Geometry and Topology
- C. Birkar
- Yuri Prokhorov
- Constantin Shramov
- Y. Odaka
- Christopher D. Hacon
- H. Blum
- O. Fujino
- Chenyang Xu
In Mathematical Physics
- C. Birkar
- Constantin Shramov
- Yuri Prokhorov
- Christopher D. Hacon
- V. Popov
- Stefano Filipazzi
- Chenyang Xu
Citations in the corpus
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- Positivity of the CM line bundle for families of K-stable klt Fano varieties (2020, unknown): “In this paper we are interested in uniformK-stability [10,25,39], which at least for smooth Fano manifold is known to be equivalent to K-stability (we should stress that the proof is via the equivalence with the existence of a Kähler-Einstein metric).”
- Jordan property for groups of birational selfmaps (2013, background): “Proposition 4.6 (cf. [Bir12, Proof of Theorem 4.1, Step 3]).”
- The dual complex of Calabi–Yau pairs (2015, unknown): “The following is essentially proved in [2,18].”