#### Vol. 15, No. 2, 2021

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

### Chen Jiang and Haidong Liu

Vol. 15 (2021), No. 2, 545–567
##### Abstract

We show the boundedness of B-pluricanonical representa- tions of lc log Calabi–Yau pairs in dimension $2$. As applica- tions, we prove the boundedness of indices of slc log Calabi–Yau pairs up to dimension $3$ and that of nonklt lc log Calabi–Yau pairs in dimension $4$.

##### Keywords
log pluricanonical representation, boundedness, index conjecture
##### Mathematical Subject Classification
Primary: 14E30
Secondary: 14E07, 14J32