Existence of flips for generalized lc pairs

Abstract

We prove the existence of flips for $\mathbb{Q}$-factorial NQC generalized lc pairs, and the cone and contraction theorems for NQC generalized lc pairs. This answers a question of C. Birkar which was conjectured by J. Han and Z. Li. As an immediate application, we show that we can run the minimal model program for $\mathbb{Q}$-factorial NQC generalized lc pairs. In particular, we complete the minimal model program for $\mathbb{Q}$-factorial NQC generalized lc pairs in dimension $\le 3$ and pseudo-effective $\mathbb{Q}$-factorial NQC generalized lc pairs in dimension $4$.

arXiv comment38 pages, v3. Comments are welcome. Proof of Theorem 1.1 has been greatly simplified

References in corpus (18)

• Termination of (many) 4-dimensional log flips
• ACC for minimal log discrepancies of exceptional singularities
• On Generalised Abundance, I
• On the connectedness principle and dual complexes for generalized pairs
• On minimal log discrepancies on varieties with fixed Gorenstein index
• Log Calabi-Yau fibrations
• Weak Zariski decompositions and log terminal models for generalized polarized pairs
• Existence and boundedness of $n$-complements
• Invariance of Plurigenera and boundedness for Generalized Pairs
• Boundedness of elliptic Calabi-Yau varieties with a rational section
• Special termination for log canonical pairs
• Boundedness of the base varieties of certain fibrations
• Cone theorem and Mori hyperbolicity
• Corrigendum: On subadditivity of the logarithmic Kodaira dimension
• Existence of log canonical modifications and its applications
• Boundedness and volume of generalised pairs
• Effective birationality for sub-pairs with real coefficients
• Number of singular points on projective surfaces

Cited by in corpus (1)

• Iitaka fibrations for dlt pairs polarized by a nef and log big divisor