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arXiv · 2408.16610

On Hyperkähler manifolds of K3$^{[n]}$-type with large Picard number

Yulieth Prieto-Montañez
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Abstract

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.

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Yulieth Prieto-Montañez. 2024-09-05. On Hyperkähler manifolds of K3$^{[n]}$-type with large Picard number. https://arxiv.org/abs/2408.16610

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