Special Lagrangians and Bridgeland stable objects beyond geometric stability conditions: the product case
Symplectic Geometry
2026-03-23 v2 Algebraic Geometry
Abstract
We construct a family of non-geometric Bridgeland stability conditions on certain wrapped Fukaya categories, using homological mirror symmetry and categorical K\"unneth formulae. These stability conditions correspond to certain holomorphic volume forms, under which we prove that every stable object admits a special Lagrangian representative. This provides the first higher-dimensional examples of stability conditions away from the large complex structure limit for which ``stable implies special Lagrangian" is proved.
Keywords
Cite
@article{arxiv.2602.03041,
title = {Special Lagrangians and Bridgeland stable objects beyond geometric stability conditions: the product case},
author = {Yu-Wei Fan},
journal= {arXiv preprint arXiv:2602.03041},
year = {2026}
}
Comments
30 pages. Comments are welcome!