Semistable $J$-equation on K\"ahler threefold

Junbang Liu

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arXiv · 2608.22674

Semistable $J$-equation on K\"ahler threefold

Junbang Liu

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Abstract

For a $3$-dimensional compact K\"ahler manifold $X$ with a pair of K\"ahler class $(\alpha,\beta)$ which is $J$-semistable, we show that the $J$-null locus of $(\alpha,\beta)$ forms a subvariety of $X$. We also give an analyic characterization of the $J$-null locus using K\"ahler currents with analytic singularities analogous to the theorem of Collins-Tosatti \cite{CT15}. As an application, we show the smooth convergence of the $J$-flow off the $J$-null locus. It gives higer order partial regularity for weak solutions of semistable $J$-equations obtained in \cite{M26b}.

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Junbang Liu. 2026-08-24. Semistable $J$-equation on K\"ahler threefold. https://arxiv.org/abs/2608.22674

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