Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Liu, Junbang
Institution: Hong Kong University of Science and Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213350134