Partial compactification of stability manifolds by massless semistable objects



Woolf, Jonathan ORCID: 0000-0002-7059-3521, Broomhead, Nathan, Pauksztello, David and Ploog, David
(2022) Partial compactification of stability manifolds by massless semistable objects. [Preprint]

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Abstract

We introduce two partial compactifications 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 classical 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 2. For these, our partial compactification can be explicitly described and related to the wall-and-chamber structure of the stability space.

Item Type: Preprint
Additional Information: Submitted to Inventiones Mathematiae (18/10/2022)
Uncontrolled Keywords: Stability conditions
Depositing User: Symplectic Admin
Date Deposited: 27 Oct 2022 16:30
Last Modified: 18 Jan 2023 19:49
DOI: 10.48550/arXiv.2208.03173
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3165696