In this article, we prove that for any Zhou valuation $\nu$, there exists a graded sequence of ideals $\mathfrak{ a}_{ \bullet}$ and a nonzero ideal $\mathfrak{ q}$ such that $\nu$ $\mathscr{ A}-$computes the jumping number $\mathrm{ lct}^{ \mathfrak{ q}}(\mathfrak{ a}_{ \bullet})$, and that for the subadditive sequence $\mathfrak{ b}^{ \varphi}_{ \bullet}$ related to a plurisubharmonic function $\varphi$, there exists a Zhou valuation which $\mathscr{ A}-$computes $\mathrm{ lct}^{ \mathfrak{ q}}(\mathfrak{ b}^{ \varphi}_{ \bullet})$, where the ``$\mathscr{ A}-$compute'' coincides with the ``compute'' in Jonsson-Musta\c{ t}\u{ a}'s Conjecture when the Zhou valuation $\nu$ is quasimonomial. There are also some results obtained for Zhou valuations, including a characterization for a valuation being a Zhou valuation, and a denseness property of the cone of Zhou valuations.
Categories: math.CV math.AG