Zhou valuations and jumping numbers

Fuente: arXiv
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Hauptverfasser: Bao, Shijie, Guan, Qi'an, Yuan, Zheng
Format: Preprint
Veröffentlicht: 2023
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author Bao, Shijie
Guan, Qi'an
Yuan, Zheng
author_facet Bao, Shijie
Guan, Qi'an
Yuan, Zheng
contents In this article, we prove that for any Zhou valuation $ν$, there exists a graded sequence of ideals $\mathfrak{a}_{\bullet}$ and a nonzero ideal $\mathfrak{q}$ such that $ν$ $\mathscr{A}-$computes the jumping number $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{a}_{\bullet})$, and that for the subadditive sequence $\mathfrak{b}^φ_{\bullet}$ related to a plurisubharmonic function $φ$, there exists a Zhou valuation which $\mathscr{A}-$computes $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{b}^φ_{\bullet})$, where the ``$\mathscr{A}-$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.
format Preprint
id arxiv_https___arxiv_org_abs_2311_06565
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Zhou valuations and jumping numbers
Bao, Shijie
Guan, Qi'an
Yuan, Zheng
Complex Variables
Algebraic Geometry
In this article, we prove that for any Zhou valuation $ν$, there exists a graded sequence of ideals $\mathfrak{a}_{\bullet}$ and a nonzero ideal $\mathfrak{q}$ such that $ν$ $\mathscr{A}-$computes the jumping number $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{a}_{\bullet})$, and that for the subadditive sequence $\mathfrak{b}^φ_{\bullet}$ related to a plurisubharmonic function $φ$, there exists a Zhou valuation which $\mathscr{A}-$computes $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{b}^φ_{\bullet})$, where the ``$\mathscr{A}-$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.
title Zhou valuations and jumping numbers
topic Complex Variables
Algebraic Geometry
url https://arxiv.org/abs/2311.06565