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arXiv · 2103.10328

Stability of some vector bundles on Hilbert schemes of points on K3 surfaces

Fabian Reede·Ziyu Zhang
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Abstract

Let $X$ be a projective K3 surfaces. In two examples where there exists a fine moduli space $M$ of stable vector bundles on $X$, isomorphic to a Hilbert scheme of points, we prove that the universal family $\mathcal{E}$ on $X\times M$ can be understood as a complete flat family of stable vector bundles on $M$ parametrized by $X$, which identifies $X$ with a smooth connected component of some moduli space of stable sheaves on $M$.

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Fabian Reede, Ziyu Zhang. 2021-12-08. Stability of some vector bundles on Hilbert schemes of points on K3 surfaces. https://doi.org/10.1007/s00209-021-02920-6

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