Mathematical Research Letters

Volume 19 (2012)

Number 2

Log-canonical models of singular pairs and its applications

Pages: 325 – 334



Yuji Odaka (Research Institute for Mathematical Sciences, Kyoto University, Japan)

Chenyang Xu (Beijing International Center of Mathematics Research, 5 Yiheyuan Road, Haidian District, Beijing 100871, China; Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, U.S.A.)


We prove the existence of the log-canonical model over a log pair $(X,\Delta)$. As an application, together withKollár’s gluing theory, we remove the assumption in the first named author’s work \cite{Odaka11}, which showsthat $K$-semistable polarized varieties can only have semi-log-canonical singularities.

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