超临界LYZ方程边界情形的除子刚性及正则性
Divisorial Rigidity and Regularity of Boundary Cases for the Supercritical LYZ Equation
- Shanghai Center for Mathematical Sciences, Fudan University（复旦大学上海数学中心）
- Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
- School of Mathematical Sciences, Key Laboratory of Mathematics and Engineering Applications (Ministry of Education), Shanghai Key Laboratory of PMMP, East China Normal University（华东师范大学数学科学学院教育部数学工程与应用关键实验室上海市PMMP重点实验室）
- 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：
本文研究紧致Kähler流形上超临界LYZ方程在稳定边界的情形，通过数值半稳定下的正性估计与除子刚性，构造了对数奇性子解，进而得到有界且补集光滑的Bedford--Taylor解。
AI中文摘要：
我们研究紧致Kähler流形上稳定边界处的超临界LYZ方程。在数值半稳定条件下，我们证明了修正nef锥上的定量正性估计。该估计意味着失稳的素除子构成一个有限例外族。假设存在光滑半子解，我们证明了在这些除子类的张成空间上，相关的相交形式是负定的。利用此刚性，我们沿其并集构造了一个对数奇性子解，并得到一个有界的Bedford--Taylor解，该解在其补集上是光滑的。
英文摘要：
We study the supercritical LYZ equation on compact Kähler manifolds at the boundary of stability. Under numerical semistability, we prove a quantitative positivity estimate on the modified nef cone. It implies that the destabilizing prime divisors form a finite exceptional family. Assuming the existence of a smooth semisubsolution, we prove that the associated intersection form is negative definite on the span of classes of these divisors. Using this rigidity, we then construct a logarithmic singular subsolution along their union and obtain a bounded Bedford--Taylor solution which is smooth on its complement.
