Log-canonical models of singular pairs and its applications
  We prove the existence of log canonical modifications for a log pair. As an application, together with Koll\"ar's gluing theory, we remove the assumption in the first named author's work [Odaka11], which shows that K-semistable polarized varieties can only have semi-log-canonical singularities. 
Yuji Odaka and Chenyang Xu
math.AG