Thurston compactifications of spaces of stability conditions on curves
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866929334941384704 |
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| author | Kikuta, Kohei Koseki, Naoki Ouchi, Genki |
| author_facet | Kikuta, Kohei Koseki, Naoki Ouchi, Genki |
| contents | In this paper, we construct a compactification of the space of Bridgeland stability conditions on a smooth projective curve, as an analogue of Thurston compactifications in Teichmüller theory.
In the case of elliptic curves, we compare our results with the classical one of the torus via homological mirror symmetry and give the Nielsen-Thurston classification of autoequivalences using the compactification.
Furthermore, we observe an interesting phenomenon in the case of the projective line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_08001 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Thurston compactifications of spaces of stability conditions on curves Kikuta, Kohei Koseki, Naoki Ouchi, Genki Algebraic Geometry Geometric Topology 14J33, 18G80, 57K20 In this paper, we construct a compactification of the space of Bridgeland stability conditions on a smooth projective curve, as an analogue of Thurston compactifications in Teichmüller theory. In the case of elliptic curves, we compare our results with the classical one of the torus via homological mirror symmetry and give the Nielsen-Thurston classification of autoequivalences using the compactification. Furthermore, we observe an interesting phenomenon in the case of the projective line. |
| title | Thurston compactifications of spaces of stability conditions on curves |
| topic | Algebraic Geometry Geometric Topology 14J33, 18G80, 57K20 |
| url | https://arxiv.org/abs/2211.08001 |