On Finiteness of B-representation and Semi-log Canonical Abundance

Abstract

We give a new proof of the finiteness of B-representations. As a consequence of the finiteness of B-representations and Kollár's gluing theory on lc centers, we prove that the (relative) abundance conjecture for slc pairs is implied by the abundance conjecture for log canonical pairs.

13 pages. Comments are welcome! Minor mistakes/typos are corrected in the version 2

References in corpus (3)

• Log pluricanonical representations and abundance conjecture
• Existence of log canonical closures
• Existence of log canonical flips and a special LMMP

Cited by in corpus (8)

• Log pluricanonical representations and abundance conjecture
• Versions of injectivity and extension theorems
• Existence of log canonical flips and a special LMMP
• Minimal model program for excellent surfaces
• Log canonical pairs with boundaries containing ample divisors
• Finiteness of log abundant log canonical pairs in log minimal model program with scaling
• On minimal model theory for log abundant lc pairs
• An abundance theorem for generalised pairs