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

Jiang, Chen; Liu, Haidong

doi:10.2140/ant.2021.15.547

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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

DOI: 10.2140/ant.2021.15.547

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 $4$ .

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Keywords

log pluricanonical representation, boundedness, index conjecture

Mathematical Subject Classification

Primary: 14E30

Secondary: 14E07, 14J32

Milestones

Received: 8 April 2020

Revised: 8 July 2020

Accepted: 11 September 2020

Published: 7 April 2021

Authors

Chen Jiang
Shanghai Center for Mathematical Sciences Fudan University Shanghai China

Haidong Liu
Beijing International Center for Mathematical Research (BICMR) Peking University Beijing China

Vol. 15, No. 2, 2021