The period-index problem for hyperkähler manifolds
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917883109441536 |
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| author | Huybrechts, Daniel |
| author_facet | Huybrechts, Daniel |
| contents | We conjecture that every unramified Brauer class $α\in \text{Br}(X)$ on a projective hyperkähler manifold $X$ satisfies $\text{ind}(α)\mid\text{per}(α)^{\dim(X)/2}$. We provide evidence for this conjecture by proving it for two large classes of projective hyperkähler manifolds: For projective hyperkähler manifolds admitting a Lagrangian fibration and for Hilbert schemes of K3 surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17604 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The period-index problem for hyperkähler manifolds Huybrechts, Daniel Algebraic Geometry We conjecture that every unramified Brauer class $α\in \text{Br}(X)$ on a projective hyperkähler manifold $X$ satisfies $\text{ind}(α)\mid\text{per}(α)^{\dim(X)/2}$. We provide evidence for this conjecture by proving it for two large classes of projective hyperkähler manifolds: For projective hyperkähler manifolds admitting a Lagrangian fibration and for Hilbert schemes of K3 surfaces. |
| title | The period-index problem for hyperkähler manifolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2411.17604 |