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

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.

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log pluricanonical representation, boundedness, index conjecture
Mathematical Subject Classification
Primary: 14E30
Secondary: 14E07, 14J32
Received: 8 April 2020
Revised: 8 July 2020
Accepted: 11 September 2020
Published: 7 April 2021
Chen Jiang
Shanghai Center for Mathematical Sciences
Fudan University
Haidong Liu
Beijing International Center for Mathematical Research (BICMR)
Peking University