Zhou valuations and jumping numbers

2023/11/11 by Bao, Shijie, Guan, Qi'an, Yuan, Zheng · 2 citations
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.06565

Abstract

In this article, we prove that for any Zhou valuation ν, there exists a graded sequence of ideals \mathfraka_\bullet and a nonzero ideal \mathfrakq such that ν \mathscrA-computes the jumping number lct^\mathfrakq(\mathfraka_\bullet), and that for the subadditive sequence \mathfrakb^φ_\bullet related to a plurisubharmonic function φ, there exists a Zhou valuation which \mathscrA-computes lct^\mathfrakq(\mathfrakb^φ_\bullet), where the ``\mathscrA-compute'' coincides with the ``compute'' in Jonsson-Mustaţă's Conjecture when the Zhou valuation ν 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.

Cited by

• The existence of valuative interpolation
• Algebraic Zhou valuations

Related

• Algebraic Zhou valuations
• Valuations and asymptotic invariants for sequences of ideals
• Tame maximal weights, relative types and valuations
• Jumping numbers of analytic multiplier ideals (with an appendix by Sébastien Boucksom)
• The existence of valuative interpolation