Contents Online
Cambridge Journal of Mathematics
Volume 11 (2023)
Number 4
Existence of flips for generalized $\operatorname{lc}$ pairs
Pages: 795 – 828
DOI: https://dx.doi.org/10.4310/CJM.2023.v11.n4.a1
Authors
Abstract
$\def\lc{\operatorname{lc}} \def\Q{\mathbb{Q}}$We prove the existence of flips for $\Q$-factorial NQC generalized lc pairs, and the cone and contraction theorems for NQC generalized $\lc$ pairs. This answers a conjecture of Han–Li–Birkar. As an immediate application, we show that we can run the minimal model program for $\Q$-factorial NQC generalized $\lc$ pairs. In particular, we complete the minimal model program for $\Q$-factorial NQC generalized $\lc$ pairs in dimension $\leq 3$ and pseudo-effective $\Q$-factorial NQC generalized $\lc$ pairs in dimension $4$.
Keywords
generalized pairs, minimal model program, flips, cone theorem
2010 Mathematics Subject Classification
, 14J35. Primary 14C20, 14E30. Secondary 14E05, 14J17, 14J30.
The authors are partially supported by NSF research grants DMS-1801851 and DMS-1952522; and by a grant from the Simons Foundation, Award Number 256202.
Received 14 February 2022
Published 29 September 2023