On Hyperkähler manifolds of K3$^{[n]}$-type with large Picard number
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912016139026432 |
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| author | Prieto-Montañez, Yulieth |
| author_facet | Prieto-Montañez, Yulieth |
| contents | Inspired by well-known examples of hyperkähler manifolds, we show that any hyperkähler manifold $X$ of K3$^{[n]}$-type with Picard number $ρ(X) \geq 4$ is always isomorphic to a moduli space of twisted stable sheaves on a K3 surface. Additionally, we provide explicit descriptions of hyperkähler manifolds of K3$^{[n]}$-type with Picard ranks below this crucial value (e.g., $ρ(X)=3$) that are not birational to such moduli spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16610 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Hyperkähler manifolds of K3$^{[n]}$-type with large Picard number Prieto-Montañez, Yulieth Algebraic Geometry Number Theory 14J50, 14E05, 14D20, 14C05 Inspired by well-known examples of hyperkähler manifolds, we show that any hyperkähler manifold $X$ of K3$^{[n]}$-type with Picard number $ρ(X) \geq 4$ is always isomorphic to a moduli space of twisted stable sheaves on a K3 surface. Additionally, we provide explicit descriptions of hyperkähler manifolds of K3$^{[n]}$-type with Picard ranks below this crucial value (e.g., $ρ(X)=3$) that are not birational to such moduli spaces. |
| title | On Hyperkähler manifolds of K3$^{[n]}$-type with large Picard number |
| topic | Algebraic Geometry Number Theory 14J50, 14E05, 14D20, 14C05 |
| url | https://arxiv.org/abs/2408.16610 |