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A smooth compactification of spaces of stability conditions: the case of the $A_{n}$-quiver
- Publication Year :
- 2023
-
Abstract
- We propose a notion of multi-scale stability conditions with the goal of providing a smooth compactification of the quotient of the space of projectivized Bridgeland stability conditions by the group of autoequivalence. For the case of the 3CY category associated with the $A_n$-quiver this goal is achieved by defining a topology and complex structure that relies on a plumbing construction. We compare this compactification to the multi-scale compactification of quadratic differentials and briefly indicate why even for the Kronecker quiver this notion needs refinement to provide a full compactification.<br />Comment: Final version to appear in Forum of Mathematics, Sigma
- Subjects :
- Mathematics - Algebraic Geometry
Mathematics - Representation Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2312.02686
- Document Type :
- Working Paper