Termination of (many) 4-dimensional log flips

Abstract

We prove that any sequence of 4-dimensional log flips that begins with a klt pair (X,D) such that -(K+D) is numerically equivalent to an effective divisor, terminates. This implies termination of flips that begin with a log Fano pair and termination of flips in a relative birational setting. We also prove termination of directed flips with big K+D. As a consequence, we prove existence of minimal models of 4-dimensional dlt pairs of general type, existence of 5-dimensional log flips, and rationality of Kodaira energy in dimension 4.

13 pages; a minor change in the proof of Thm.4.3

References in corpus (2)

• On the existence of flips
• Termination of log flips in dimension 4

Cited by in corpus (13)

• Introduction to the log minimal model program for log canonical pairs
• On existence of log minimal models
• On singular Calogero-Moser spaces
• Globally +-regular varieties and the minimal model program for threefolds in mixed characteristic
• The Minimal Model Program for threefolds in characteristic five
• On the number of minimal models of a log smooth threefold
• On a connectedness principle of Shokurov-Kollár type
• On the semiampleness of the positive part of CKM Zariski decompositions
• Existence of flips for generalized lc pairs
• On the termination of flips for log canonical generalized pairs
• Connectedness principle for $3$-folds in characteristic $p>5$
• On termination of flips and exceptionally non-canonical singularities
• Lectures on birational geometry