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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2304.02609 |
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| _version_ | 1866929229537476608 |
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| author | Saccà, Giulia |
| author_facet | Saccà, Giulia |
| contents | This article studies moduli spaces of Bridgeland semistable objects in the Kuznetsov component of a cubic fourfold that don't admit a symplectic resolution, i.e., moduli spaces of objects with non-primitve Mukai vector v=mv_0 that is not of OG10-type and where v_0^2 >0. For a generic stability condition, it is shown that these moduli spaces are projective irreducible symplectic varieties with factorial terminal singularities and that their deformation class is uniquely determined by the integers m and v_0^2. On the one hand, this generalizes the results of arXiv:1703.10839, arXiv:1912.06935, arXiv:2007.14108, which deal with moduli spaces of objects in the Kuznetsov component of a cubic fourfold which are smooth or of OG10-type; on the other hand, this extends to the Kuznetsov component of a cubic fourfold the results of arXiv:1802.01182, arXiv:2012.10649, on Gieseker moduli spaces of sheaves on K3 surfaces with non-primitive Mukai vector. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02609 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Moduli spaces on Kuznetsov components are Irreducible Symplectic Varieties Saccà, Giulia Algebraic Geometry 14D22, 14J42, 13D09 This article studies moduli spaces of Bridgeland semistable objects in the Kuznetsov component of a cubic fourfold that don't admit a symplectic resolution, i.e., moduli spaces of objects with non-primitve Mukai vector v=mv_0 that is not of OG10-type and where v_0^2 >0. For a generic stability condition, it is shown that these moduli spaces are projective irreducible symplectic varieties with factorial terminal singularities and that their deformation class is uniquely determined by the integers m and v_0^2. On the one hand, this generalizes the results of arXiv:1703.10839, arXiv:1912.06935, arXiv:2007.14108, which deal with moduli spaces of objects in the Kuznetsov component of a cubic fourfold which are smooth or of OG10-type; on the other hand, this extends to the Kuznetsov component of a cubic fourfold the results of arXiv:1802.01182, arXiv:2012.10649, on Gieseker moduli spaces of sheaves on K3 surfaces with non-primitive Mukai vector. |
| title | Moduli spaces on Kuznetsov components are Irreducible Symplectic Varieties |
| topic | Algebraic Geometry 14D22, 14J42, 13D09 |
| url | https://arxiv.org/abs/2304.02609 |