Log canonical pairs with boundaries containing ample divisors

Abstract

Let $(X,\Delta )$ be a projective log canonical pair such that $\Delta \ge A$ where $A\ge 0$ is an ample $\mathbb{R}$-divisor. We prove that either $(X,\Delta )$ has a good minimal model or a Mori fibre space. Moreover, if $X$ is $\mathbb{Q}$-factorial, then any Log Minimal Model Program on $K_X+\Delta$ with scaling terminates. As an application we prove that a log Fano type variety $X$ with $\mathbb{Q}$-factorial log canonical singularities is a Mori dream space.

40 pages

References in corpus (3)

• Introduction to the log minimal model program for log canonical pairs
• On the anti-canonical ring and varieties of Fano type
• Remarks on special kinds of the relative log minimal model program

Cited by in corpus (3)

• Log abundance of the moduli b-divisors of lc-trivial fibrations
• On minimal model theory for log abundant lc pairs
• An abundance theorem for generalised pairs