Stability conditions on K3 surfaces via mass of spherical objects
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910912792756224 |
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| author | Kikuta, Kohei Koseki, Naoki Ouchi, Genki |
| author_facet | Kikuta, Kohei Koseki, Naoki Ouchi, Genki |
| contents | We prove that a stability condition on a K3 surface is determined by the masses of spherical objects up to a natural $\mathbb{C}$-action. This is motivated by the result of Huybrechts and the recent proposal of Bapat-Deopurkar-Licata on the construction of a compactification of a stability manifold. We also construct lax stability conditions in the sense of Broomhead-Pauksztello-Ploog-Woolf associated to spherical bundles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_12253 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability conditions on K3 surfaces via mass of spherical objects Kikuta, Kohei Koseki, Naoki Ouchi, Genki Algebraic Geometry Geometric Topology 14F08, 14J28, 57K20 We prove that a stability condition on a K3 surface is determined by the masses of spherical objects up to a natural $\mathbb{C}$-action. This is motivated by the result of Huybrechts and the recent proposal of Bapat-Deopurkar-Licata on the construction of a compactification of a stability manifold. We also construct lax stability conditions in the sense of Broomhead-Pauksztello-Ploog-Woolf associated to spherical bundles. |
| title | Stability conditions on K3 surfaces via mass of spherical objects |
| topic | Algebraic Geometry Geometric Topology 14F08, 14J28, 57K20 |
| url | https://arxiv.org/abs/2504.12253 |