J方程的最优去稳定化子簇的有限性与刚性
Finiteness and rigidity of optimal destabilizing subvarieties for the J-equation
- Aarhus University（奥胡斯大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究证明J方程无光滑解时，紧致Kähler流形上最优去稳定化曲线与除子有限，三维流形上所有此类子簇无条件有限，还刻画其轨迹并证明最优闭链的刚性准则。
AI中文摘要：
我们证明，当J方程不存在光滑解时，任意维紧致Kähler流形上始终仅存在有限个起阻碍作用的最优去稳定化曲线和除子。对于三维流形，这确立了所有最优去稳定化子簇的无条件有限性。我们进一步刻画这些最优子簇的并集，证明它们包含于自然连续性路径失去局部光滑紧性的轨迹中。最后，为处理既非曲线也非除子的子簇，我们证明一个刚性准则，该准则阻止最优闭链在紧致单参数族中移动，并对其形变与对称性性质有进一步推论。
英文摘要：
We prove that when the J-equation does not admit a smooth solution, there is always only a finite number of obstructing optimally destabilizing curves and divisors on compact Kähler manifolds of any dimension. For threefolds, this establishes the unconditional finiteness of all optimally destabilizing subvarieties. We moreover characterize the union of these optimal subvarieties, proving that they are contained in the locus where a natural continuity path loses local smooth compactness. Finally, to address subvarieties that are neither curves nor divisors, we prove a rigidity criterion which prevents optimal cycles from moving in compact one-parameter families, with further consequences for their deformation and symmetry properties.
