Perverse schobers, stability conditions and quadratic differentials
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914848356433920 |
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| author | Christ, Merlin Haiden, Fabian Qiu, Yu |
| author_facet | Christ, Merlin Haiden, Fabian Qiu, Yu |
| contents | We develop a unified approach for identifying spaces of stability conditions of triangulated categories arising from weighted marked surfaces with moduli spaces of quadratic differentials. This approach is based on the notion of a perverse schober (perverse sheaf of triangulated categories) and their triangulated categories of global sections. Under suitable conditions on the perverse schober, we identify mixed-angulations and their flips with finite-length hearts and their tilts, which then leads to the identification of moduli spaces. As an application we obtain a generalization of the results of Bridgeland--Smith to quadratic differentials with arbitrary singularity type (zero/pole/exponential). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_18249 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Perverse schobers, stability conditions and quadratic differentials Christ, Merlin Haiden, Fabian Qiu, Yu Representation Theory Algebraic Geometry Geometric Topology We develop a unified approach for identifying spaces of stability conditions of triangulated categories arising from weighted marked surfaces with moduli spaces of quadratic differentials. This approach is based on the notion of a perverse schober (perverse sheaf of triangulated categories) and their triangulated categories of global sections. Under suitable conditions on the perverse schober, we identify mixed-angulations and their flips with finite-length hearts and their tilts, which then leads to the identification of moduli spaces. As an application we obtain a generalization of the results of Bridgeland--Smith to quadratic differentials with arbitrary singularity type (zero/pole/exponential). |
| title | Perverse schobers, stability conditions and quadratic differentials |
| topic | Representation Theory Algebraic Geometry Geometric Topology |
| url | https://arxiv.org/abs/2303.18249 |