Abstract: We study the geometry of the triples which consist of a usual pair and a pseudoeffective divisor. We prove that there exists a quasi-monomial valuation which computes the log canonical threshold of the triple if the triple is potentially klt. As a by product, we show that in such a case, we can run the -K-MMP. This is based on the joint work with S.Jang, D.Kim, and D.Lee.
