A twisted derived category of hyper-Kähler varieties of $K3^{[n]}$-type
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909655232413696 |
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| author | Zhang, Ruxuan |
| author_facet | Zhang, Ruxuan |
| contents | We conjecture that a natural twisted derived category of any hyper-Kähler variety of $K3^{[n]}$-type is controlled by its Markman-Mukai lattice. We prove the conjecture under numerical constraints, and our proof relies heavily on Markman's projectively hyperholomorphic bundle and a recently proven twisted version of the D-equivalence conjecture.
In particular, we prove that any two fine moduli spaces of stable sheaves on a $K3$ surface are derived equivalent if they have the same dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A twisted derived category of hyper-Kähler varieties of $K3^{[n]}$-type Zhang, Ruxuan Algebraic Geometry 14JJ42, 14D20, 14F08 We conjecture that a natural twisted derived category of any hyper-Kähler variety of $K3^{[n]}$-type is controlled by its Markman-Mukai lattice. We prove the conjecture under numerical constraints, and our proof relies heavily on Markman's projectively hyperholomorphic bundle and a recently proven twisted version of the D-equivalence conjecture. In particular, we prove that any two fine moduli spaces of stable sheaves on a $K3$ surface are derived equivalent if they have the same dimension. |
| title | A twisted derived category of hyper-Kähler varieties of $K3^{[n]}$-type |
| topic | Algebraic Geometry 14JJ42, 14D20, 14F08 |
| url | https://arxiv.org/abs/2502.02143 |