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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2603.29053 |
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| _version_ | 1866915900952674304 |
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| author | Selvaggi, Ian |
| author_facet | Selvaggi, Ian |
| contents | We give a structure result on the set of locally constant stability conditions, $\operatorname{Stab}(\mathcal{D}/R)$, defined by Halpern-Leistner-Robotis showing that it has the structure of a complex manifold, in total analogy with Bridgeland's work. As a consequence, we show that the property of having relative mass-hom bounds and the existence of good moduli spaces depends only on the connected components of $\operatorname{Stab}(\mathcal{D}/R)$. Lastly, we observe that the datum of a locally constant stability condition is equivalent to that of a flat family of stability conditions, as described by Bayer et al. in the context of noncommutative algebraic geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29053 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deformations of locally constant stability conditions and good moduli spaces Selvaggi, Ian Algebraic Geometry We give a structure result on the set of locally constant stability conditions, $\operatorname{Stab}(\mathcal{D}/R)$, defined by Halpern-Leistner-Robotis showing that it has the structure of a complex manifold, in total analogy with Bridgeland's work. As a consequence, we show that the property of having relative mass-hom bounds and the existence of good moduli spaces depends only on the connected components of $\operatorname{Stab}(\mathcal{D}/R)$. Lastly, we observe that the datum of a locally constant stability condition is equivalent to that of a flat family of stability conditions, as described by Bayer et al. in the context of noncommutative algebraic geometry. |
| title | Deformations of locally constant stability conditions and good moduli spaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2603.29053 |