On existence of log minimal models II

By C. Birkar. 2009

81 citations recorded by the source corpus.

Abstract We prove that the existence of log minimal models in dimension d essentially implies the LMMP with scaling in dimension d. As a consequence we prove that a weak nonvanishing conjecture in dimension d implies the minimal model conjecture in dimension d.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/190e63c5f97435d9edf31374855c2a6452a2d04a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. J. Waldron
2. C. Birkar
3. Y. Odaka
4. Christopher D. Hacon
5. H. Blum
6. O. Fujino
7. F. Catanese
8. Ingrid Bauer

Citations in the corpus

• Log pluricanonical representations and abundance conjecture (2011, unknown): “that KX+∆ ∼R,Z M. Proof. Apply Conjecture 5.1 and Remark 5.2 to the generic fiber of f. Then, by [BCHM, Lemma 3.2.1], we obtain M with the required properties. We give a small remark on Birkar’s paper [B1]. Remark 5.4 (Absolute versus relative). Let f: X→ Zbe a projective morphism between projective ”
• Existence of Mori fibre spaces for 3-folds in char $p$ (2014, background): “(4) assume KX + B is nef, ∆ ∈ L, and that Xi 99K Xi+1/Zi is a sequence of KX + ∆-flips which are KX + B-trivial and X = X1; then for any curve Γ on any Xi, we have (KXi + Bi) · Γ > α if (KXi + Bi) · Γ > 0 where Bi is the birational transform of B; (5) in addition to the assumptions of (4) suppose th”