Geodesic
A smooth compactification of spaces of stability conditions: the case of the $A_{n}$-quiver
Forum of Mathematics, Sigma, Tome 12 (2024)

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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. 
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     author = {Anna Barbieri and Martin M\"oller and Jeonghoon So},
     title = {A smooth compactification of spaces of stability conditions: the case of the $A_{n}$-quiver},
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Anna Barbieri; Martin Möller; Jeonghoon So. A smooth compactification of spaces of stability conditions: the case of the $A_{n}$-quiver. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.106

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