제목: Existence of computing valuation of the log canonical threshold of a pseudo-effective divisor

초록: In this talk, we give a valuative description to log canonical threshold of an ideal sheaf, and a graded sequence of ideal sheaves. Moreover, we give the definition of log canonical threshold for a pseudo-effective divisor $D$. One of the major theorems of Jonsson-Mustata is that there is a valuation computing the log canonical threshold of a graded sequence of ideals. However, we can not mimic the proof for the log canonical threshold for a pseudo-effective divisor because of the lack of continuity of asymptotic valuation function for pseudo-effective divisor. In this talk, we give the method on how to overcome the difficulty and prove the existence of computing (quasi-monomial) valuation of the log canonical threshold for a pseudo-effective divisor. Lastly, by the result, we prove for a pklt triple $(X,\Delta,D)$, there is a $\varepsilon>0$ such that $(X,\Delta,(1+\varepsilon)D)$ is also pklt.