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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2406.19361 |
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| _version_ | 1866909693890265088 |
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| author | Guo, Hanfei Liu, Zhiyu |
| author_facet | Guo, Hanfei Liu, Zhiyu |
| contents | In this paper, we provide new examples of 1-obstructed and atomic sheaves on an infinite series of locally complete families of projective hyper-Kähler manifolds. More precisely,
(1) we prove that the fixed loci of the natural anti-symplectic involutions on the moduli spaces of stable objects in the Kuznetsov component $\mathcal{K}u(X)$ of a Gushel--Mukai fourfold $X$ are 1-obstructed Lagrangian submanifolds,
(2) we construct a family of immersed atomic Lagrangian submanifolds on each moduli space of stable objects in $\mathcal{K}u(X)$, and
(3) we construct non-rigid projectively hyperholomorphic twisted bundles on any hyper-Kähler manifold of $\mathrm{K3^{[n]}}$-type for infinitely many $n$.
Additionally, we discuss examples of atomic Lagrangian submanifolds satisfying $b_1=20$ in a family of hyper-Kähler manifolds of $\mathrm{K3^{[2]}}$-type, as well as atomic sheaves supported on non-atomic Lagrangians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19361 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Atomic sheaves on hyper-Kähler manifolds via Bridgeland moduli spaces Guo, Hanfei Liu, Zhiyu Algebraic Geometry In this paper, we provide new examples of 1-obstructed and atomic sheaves on an infinite series of locally complete families of projective hyper-Kähler manifolds. More precisely, (1) we prove that the fixed loci of the natural anti-symplectic involutions on the moduli spaces of stable objects in the Kuznetsov component $\mathcal{K}u(X)$ of a Gushel--Mukai fourfold $X$ are 1-obstructed Lagrangian submanifolds, (2) we construct a family of immersed atomic Lagrangian submanifolds on each moduli space of stable objects in $\mathcal{K}u(X)$, and (3) we construct non-rigid projectively hyperholomorphic twisted bundles on any hyper-Kähler manifold of $\mathrm{K3^{[n]}}$-type for infinitely many $n$. Additionally, we discuss examples of atomic Lagrangian submanifolds satisfying $b_1=20$ in a family of hyper-Kähler manifolds of $\mathrm{K3^{[2]}}$-type, as well as atomic sheaves supported on non-atomic Lagrangians. |
| title | Atomic sheaves on hyper-Kähler manifolds via Bridgeland moduli spaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2406.19361 |