Stability Conditions and Moduli Spaces on Kuznetsov Component of Cubic Fivefolds
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917202084495360 |
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| author | Liu, Peize |
| author_facet | Liu, Peize |
| contents | We study the Kuznetsov component of cubic fivefolds via their quadric fibration model, and construct a family of Serre-invariant Bridgeland stability conditions on it. For every primitive numerical class, we prove that the associated Bridgeland moduli space contains a non-empty smooth locus, on which the restriction to a general hyperplane section preserves stability. As a consequence, we obtain Lagrangian immersions into hyper-Kähler varieties arising as moduli spaces on the Kuznetsov component of cubic fourfolds, generalizing a geometric construction of Illiev-Manivel, which realizes the Fano surface of planes of the cubic fivefold as a Lagrangian subvariety in a hyper-Kähler fourfold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21454 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability Conditions and Moduli Spaces on Kuznetsov Component of Cubic Fivefolds Liu, Peize Algebraic Geometry We study the Kuznetsov component of cubic fivefolds via their quadric fibration model, and construct a family of Serre-invariant Bridgeland stability conditions on it. For every primitive numerical class, we prove that the associated Bridgeland moduli space contains a non-empty smooth locus, on which the restriction to a general hyperplane section preserves stability. As a consequence, we obtain Lagrangian immersions into hyper-Kähler varieties arising as moduli spaces on the Kuznetsov component of cubic fourfolds, generalizing a geometric construction of Illiev-Manivel, which realizes the Fano surface of planes of the cubic fivefold as a Lagrangian subvariety in a hyper-Kähler fourfold. |
| title | Stability Conditions and Moduli Spaces on Kuznetsov Component of Cubic Fivefolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.21454 |