AI 中文总结
针对连通光滑复射影曲面，证明Arcara–Miles猜想的有效除子版本及其严格类比，揭示线丛半稳定失效由负有效除子检测，相关数值条件与整数标度稳定性等价。
AI 中文摘要
设X为连通光滑复射影曲面，我们证明了Arcara–Miles猜想的有效除子版本及其严格类比。对每个除子型Bridgeland稳定性条件，线丛或其相关位移的不稳定或半稳定失效，分别由与非零有效Cartier除子C相关的自然子对象检测，其中C满足C²<0。证明结合了极小秩去稳定子、斜率Harder–Narasimhan滤子、Bogomolov–Gieseker不等式，以及迫使极小秩为1的有序洛伦兹部分和估计。由此，线丛或其相关位移的严格半稳定由负有效除子检测，且由扭曲变形Hermitian–Yang–Mills方程产生的数值半稳定条件等价于所有整数标度下的稳定性。
英文摘要
Let $X$ be a connected smooth complex projective surface. We prove an effective-divisor version of the Arcara--Miles conjecture, together with its strict analogue. For every divisorial Bridgeland stability condition, failure of stability, respectively semistability, of a line bundle or its relevant shift is detected by a natural subobject associated with a non-zero effective Cartier divisor $C$ satisfying $C^2<0$. The proof combines minimal-rank destabilizers, slope Harder--Narasimhan filtrations, the Bogomolov--Gieseker inequality, and an ordered Lorentzian partial-sum estimate that forces the minimal rank to be one. Consequently, strict semistability of a line bundle or its relevant shift is detected by a negative effective divisor, and a numerical semistability condition arising from the twisted deformed Hermitian--Yang--Mills equation is equivalent to stability under all integral scalings.
Comments33 pages
