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Generalized Gauduchon metrics on compact complex spaces
Abstract
Let X be an irreducible reduced compact complex space of dimension n, and let ω be a Hermitian metric on X. For each 1≤ k≤ n−1, we prove that there exist a constant ck and a smooth positive function ρ on Xreg such that ii∂∂̅(ρωk)∧ωn−k−1=ckρωn. The function ρ is bounded above and bounded away from zero. The constant ck is unique, and ρ is unique up to a positive multiple among bounded smooth positive solutions. We also prove that the full sign set {−1,0,1} of the generalized Gauduchon constants ck on a compact complex manifold is preserved by finite sequences of blow-ups with smooth centers.
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BibTeX
@misc{chen2026generalized,
title = {{Generalized Gauduchon metrics on compact complex spaces}},
author = {Yong Chen and Xi Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13005},
eprint = {2610.13005},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13005},
}
RIS
TY - UNPB
TI - Generalized Gauduchon metrics on compact complex spaces
AU - Yong Chen
AU - Xi Zhang
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13005
UR - https://arxiv.org/abs/2610.13005
AB - Let X be an irreducible reduced compact complex space of dimension n, and let ω be a Hermitian metric on X. For each 1≤ k≤ n−1, we prove that there exist a constant c_k and a smooth positive function ρ on X_reg such that ii∂∂̅(ρω^k)∧ω^n−k−1=c_kρω^n. The function ρ is bounded above and bounded away from zero. The constant c_k is unique, and ρ is unique up to a positive multiple among bounded smooth positive solutions. We also prove that the full sign set {−1,0,1} of the generalized Gauduchon constants c_k on a compact complex manifold is preserved by finite sequences of blow-ups with smooth centers.
ER -