A note on Kollár valuations

Yuchen Liu; Chenyang Xu

doi:10.1007/s11425-024-2310-2

A note on Kollár valuations

Yuchen Liu
, Chenyang Xu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the set of Kollár valuations in the dual complex of a klt singularity with a fixed complement is path connected. We also classify the case when the dual complex is one-dimensional.

Original language	English (US)
Pages (from-to)	1801-1808
Number of pages	8
Journal	Science China Mathematics
Volume	69
Issue number	7
DOIs	https://doi.org/10.1007/s11425-024-2310-2
State	Published - Jul 2026

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

14B05
14E30
Kollár valuations
dual complex
finite generation
klt singularities

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10.1007/s11425-024-2310-2

Cite this

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title = "A note on Koll{\'a}r valuations",

abstract = "We prove the set of Koll{\'a}r valuations in the dual complex of a klt singularity with a fixed complement is path connected. We also classify the case when the dual complex is one-dimensional.",

keywords = "14B05, 14E30, Koll{\'a}r valuations, dual complex, finite generation, klt singularities",

author = "Yuchen Liu and Chenyang Xu",

note = "Publisher Copyright: {\textcopyright} Science China Press 2024.",

year = "2026",

month = jul,

doi = "10.1007/s11425-024-2310-2",

language = "English (US)",

volume = "69",

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T1 - A note on Kollár valuations

AU - Liu, Yuchen

AU - Xu, Chenyang

N1 - Publisher Copyright: © Science China Press 2024.

PY - 2026/7

Y1 - 2026/7

N2 - We prove the set of Kollár valuations in the dual complex of a klt singularity with a fixed complement is path connected. We also classify the case when the dual complex is one-dimensional.

AB - We prove the set of Kollár valuations in the dual complex of a klt singularity with a fixed complement is path connected. We also classify the case when the dual complex is one-dimensional.

KW - 14B05

KW - 14E30

KW - Kollár valuations

KW - dual complex

KW - finite generation

KW - klt singularities

UR - https://www.scopus.com/pages/publications/85196427961

UR - https://www.scopus.com/pages/publications/85196427961#tab=citedBy

U2 - 10.1007/s11425-024-2310-2

DO - 10.1007/s11425-024-2310-2

M3 - Article

AN - SCOPUS:85196427961

SN - 1674-7283

VL - 69

SP - 1801

EP - 1808

JO - Science China Mathematics

JF - Science China Mathematics

IS - 7

ER -

A note on Kollár valuations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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