Partial compactification of stability manifolds via massless semistable objects
Abstract
We introduce two extensions of the space of Bridgeland stability conditions of a triangulated category. First we consider lax stability conditions where semistable objects are allowed to have mass zero but still have a phase. The subcategory of massless objects is thick and there is an induced Bridgeland stability on the quotient category. We study deformations of lax stability conditions. Second we consider the space arising by identifying lax stability conditions which are deformation-equivalent with fixed charge. This second space is stratified by stability spaces of Verdier quotients of the triangulated category by thick subcategories of massless objects. We illustrate our results through examples in which the Grothendieck group has rank . For these, our extended stability spaces can be explicitly described and related to the wall-and-chamber structure of the stability space.
Cite
@article{arxiv.2208.03173,
title = {Partial compactification of stability manifolds via massless semistable objects},
author = {Nathan Broomhead and David Pauksztello and David Ploog and Jon Woolf},
journal= {arXiv preprint arXiv:2208.03173},
year = {2026}
}
Comments
61 pages, 6 figures. We have revised the definition of the lax support property to deal with a counterexample to one of the results in version 1; we discuss this counterexample in Section 10.9. This new definition simplifies some of the proofs