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arXiv · 2312.02686

A smooth compactification of spaces of stability conditions: the case of the $A_{n}$-quiver

Anna Barbieri·Martin Möller·Jeonghoon So
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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.

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Anna Barbieri, Martin Möller, Jeonghoon So. 2023-12-05. A smooth compactification of spaces of stability conditions: the case of the $A_{n}$-quiver. https://arxiv.org/abs/2312.02686

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