J方程的边界情形：除子刚性与全局$C^0$估计
Boundary Cases of the $J$-Equation: Divisorial Rigidity and a Global $C^0$ Estimate
- Shanghai Center for Mathematical Sciences, Fudan University（复旦大学上海数学中心）
- School of Mathematical Sciences, Fudan University（复旦大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对J方程稳定性条件的两类边界情形，通过分析不稳定素除子的例外族性质、修正nef估计及近似扭曲方程的全局$C^0$估计，构造出J方程的有势Bedford-Taylor解。
AI中文摘要：
我们研究J方程稳定性条件的两种边界情形。首先，在J半稳定条件下，证明了不稳定素除子构成Boucksom意义下的例外族，且存在远离它们的一致数值间隙，相关修正 nef 估计可消除Liu在文献[Liu2026Boundary]中工作的J-大假设。其次，在光滑边界锥条件下，对近似扭曲J方程的解得到一致全局$C^0$估计，由此构造出J方程的有势Bedford-Taylor解，其在不稳定素除子外光滑。
英文摘要：
We study two boundary cases of the stability condition for the $J$-equation. First, under the $J$-semistable condition, we show that the destabilizing prime divisors form an exceptional family in the sense of Boucksom, with a uniform numerical gap away from them. The related modified nef estimate can remove the $J$-big assumption in Liu's work~\cite{Liu2026Boundary}. Second, under the smooth boundary cone condition, we obtain a uniform global $C^0$ estimate for solutions of the approximating twisted $J$-equations. As a consequence, we construct a bounded-potential Bedford--Taylor solution of the $J$-equation, which is smooth outside the destabilizing prime divisors.
