ScalingStacks

Remark 5.26 . [04G5]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Remark 5.26.

In Definition 3.32, the Thomas-Yau semistability makes use of distinguished triangles for all almost calibrated Lagrangian objects, not just those with |θ|≤π2−ϵ|\theta|\leq\frac{\pi}{2}-\epsilon. This makes the Thomas-Yau semistability a priori stronger than the semistable situation of the above dichotomy. We expect from the Thomas-Yau-Joyce picture that both stability notions are actually equivalent under our initial assumption that there is a representative L0L_{0} with |θ|<π2−ϵ|\theta|<\frac{\pi}{2}-\epsilon. But for our main purpose, that Thomas-Yau semistability implies the existence of special Lagrangians, we do not mind Thomas-Yau semistability being stronger than necessary.

Original mathematics by the credited authors. Source-backed reader collection; mathematical self-containment is not assessed.