Lagrangian families of Bridgeland moduli spaces from Gushel-Mukai fourfolds
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915174302089216 |
|---|---|
| author | Feyzbakhsh, Soheyla Guo, Hanfei Liu, Zhiyu Zhang, Shizhuo |
| author_facet | Feyzbakhsh, Soheyla Guo, Hanfei Liu, Zhiyu Zhang, Shizhuo |
| contents | Let $X$ be a very general Gushel-Mukai (GM) variety of dimension $n\geq 4$, and let $Y$ be a smooth hyperplane section. There are natural pull-back and push-forward functors between the semi-orthogonal components (known as the Kuznetsov components) of the derived categories of $X$ and $Y$. In this paper, we prove that the Bridgeland stability of objects is preserved by both pull-back and push-forward functors. We then explore various applications of this result, such as constructing an $8$-dimensional smooth family of Lagrangian subvarieties for each moduli space of stable objects in the Kuznetsov component of a general GM fourfold and proving the projectivity of the moduli spaces of semistable objects of any class in the Kuznetsov component of a general GM threefold, as conjectured by Perry, Pertusi, and Zhao. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11598 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lagrangian families of Bridgeland moduli spaces from Gushel-Mukai fourfolds Feyzbakhsh, Soheyla Guo, Hanfei Liu, Zhiyu Zhang, Shizhuo Algebraic Geometry Primary 14F08, secondary 14J42, 14J45, 14D20, 14D23 Let $X$ be a very general Gushel-Mukai (GM) variety of dimension $n\geq 4$, and let $Y$ be a smooth hyperplane section. There are natural pull-back and push-forward functors between the semi-orthogonal components (known as the Kuznetsov components) of the derived categories of $X$ and $Y$. In this paper, we prove that the Bridgeland stability of objects is preserved by both pull-back and push-forward functors. We then explore various applications of this result, such as constructing an $8$-dimensional smooth family of Lagrangian subvarieties for each moduli space of stable objects in the Kuznetsov component of a general GM fourfold and proving the projectivity of the moduli spaces of semistable objects of any class in the Kuznetsov component of a general GM threefold, as conjectured by Perry, Pertusi, and Zhao. |
| title | Lagrangian families of Bridgeland moduli spaces from Gushel-Mukai fourfolds |
| topic | Algebraic Geometry Primary 14F08, secondary 14J42, 14J45, 14D20, 14D23 |
| url | https://arxiv.org/abs/2404.11598 |