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arXiv · 2103.09661

Stable Sheaves on K3 Surfaces via Wall-Crossing

Alessio Bottini
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Abstract

We give a new proof of the following theorem: moduli spaces of stable complexes on a complex projective K3 surface, with primitive Mukai vector and with respect to a generic Bridgeland stability condition, are hyperk\"{a}hler varieties of $\mathrm{K3}^{[n]}$-type of expected dimension. We use derived equivalences, deformations and wall-crossing for Bridgeland stability to reduce to the case of the Hilbert scheme of points.

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Alessio Bottini. 2021-03-17. Stable Sheaves on K3 Surfaces via Wall-Crossing. https://arxiv.org/abs/2103.09661

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