A smooth compactification of spaces of stability conditions: the case of the $A_{n}$-quiver
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929510043090944 |
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| author | Barbieri, Anna Möller, Martin So, Jeonghoon |
| author_facet | Barbieri, Anna Möller, Martin So, Jeonghoon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02686 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A smooth compactification of spaces of stability conditions: the case of the $A_{n}$-quiver Barbieri, Anna Möller, Martin So, Jeonghoon Algebraic Geometry Representation Theory 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. |
| title | A smooth compactification of spaces of stability conditions: the case of the $A_{n}$-quiver |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2312.02686 |