Zhou valuations and jumping numbers

Abstract

In this article, we prove that for any Zhou valuation $\hat{I}½$, there exists a graded sequence of ideals ${\mathfrak{a}}_{\bullet }$ and a nonzero ideal $\mathfrak{q}$ such that $\hat{I}½$ $\mathcal{A}-$computes the jumping number ${\mathrm{lct}}^{\mathfrak{q}}({\mathfrak{a}}_{\bullet })$, and that for the subadditive sequence ${\mathfrak{b}}^{\ddot{I}}{†}_{\bullet }$ related to a plurisubharmonic function $\ddot{I}†$, there exists a Zhou valuation which $\mathcal{A}-$computes ${\mathrm{lct}}^{\mathfrak{q}}({\mathfrak{b}}^{\ddot{I}}{†}_{\bullet })$, where the ``$\mathcal{A}-$compute'' coincides with the ``compute'' in Jonsson-Mustaţă's Conjecture when the Zhou valuation $\hat{I}½$ 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.

26 pages, all comments are welcome!