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Local-to-global maximality for plurisubharmonic functions with locally analytic singularities
Abstract
We prove that a locally maximal plurisubharmonic function on a domain in bCn, n≥2, is maximal if it has locally analytic singularities with a two-sided locally bounded remainder. Using McAdam's theorem, we show that local maximality forces the analytic spread of each defining ideal to be less than n. We use normalized blow-ups and Siu's analyticity theorem to compare singularities through generic divisorial Lelong numbers. We also obtain a criterion for maximality in terms of maximality outside the pole set and the analytic spread of the local defining ideals.
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BibTeX
@misc{do2026localtoglobal,
title = {{Local-to-global maximality for plurisubharmonic functions with locally analytic singularities}},
author = {Thai Duong Do and Pham Hoang Hiep},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05937},
eprint = {2610.05937},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05937},
}
RIS
TY - UNPB
TI - Local-to-global maximality for plurisubharmonic functions with locally analytic singularities
AU - Thai Duong Do
AU - Pham Hoang Hiep
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.05937
UR - https://arxiv.org/abs/2610.05937
AB - We prove that a locally maximal plurisubharmonic function on a domain in bC^n, n≥2, is maximal if it has locally analytic singularities with a two-sided locally bounded remainder. Using McAdam's theorem, we show that local maximality forces the analytic spread of each defining ideal to be less than n. We use normalized blow-ups and Siu's analyticity theorem to compare singularities through generic divisorial Lelong numbers. We also obtain a criterion for maximality in terms of maximality outside the pole set and the analytic spread of the local defining ideals.
ER -