Boundedness of log pluricanonical representations of log Calabi-Yau pairs in dimension 2

Abstract

We show the boundedness of B-pluricanonical representations of lc log Calabi-Yau pairs in dimension 2. As applications, we prove the boundedness of indices of slc log Calabi-Yau pairs up to dimension 3 and that of non-klt lc log Calabi-Yau pairs in dimension 4.