PreprintCC BY 4.0arXiv
Finiteness of null subvarieties and optimal destabilizers for the J-equation
Abstract
Let X be a compact Kähler manifold and (α,β) be a pair of Kähler classes. We show that when (α,β) is J-semistable, the collection of positive-dimensional irreducible J-null subvarieties is finite. We also obtain a uniform positive lower bound for the normalized J-slope of every irreducible non-J-null subvariety. This confirms the finiteness and uniform-gap expectation of Khalid-Sjöström Dyrefelt \cite[Section 1.2, Theorem 1.5; Remark 1.8]{KSD26}. As a corollary, we show that the collection of optimal destabilizers is finite when the stability threshold is nonpositive.
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BibTeX
@misc{liu2026finiteness,
title = {{Finiteness of null subvarieties and optimal destabilizers for the J-equation}},
author = {Junbang Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14713},
eprint = {2609.14713},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14713},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finiteness of null subvarieties and optimal destabilizers for the J-equation
AU - Junbang Liu
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.14713
UR - https://arxiv.org/abs/2609.14713
AB - Let X be a compact Kähler manifold and (α,β) be a pair of Kähler classes. We show that when (α,β) is J-semistable, the collection of positive-dimensional irreducible J-null subvarieties is finite. We also obtain a uniform positive lower bound for the normalized J-slope of every irreducible non-J-null subvariety. This confirms the finiteness and uniform-gap expectation of Khalid-Sjöström Dyrefelt \cite[Section 1.2, Theorem 1.5; Remark 1.8]{KSD26}. As a corollary, we show that the collection of optimal destabilizers is finite when the stability threshold is nonpositive.
ER -