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arXiv · 2109.07425

Moduli of sheaves on $K3$'s and higher dimensional HK varieties

Kieran G. O'Grady
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Abstract

We review a proof of the well know result stating that moduli spaces of stable sheaves with fixed Chern character on a polarized $K3$ surface are deformations of a hyperk\"ahler variety of Type $K3^{[n]}$ (if a suitable numerical hypothesis is satisfied). In a recent work we have adapted that proof in order to prove results on moduli of vector bundles on polarized hyperk\"ahler varieties of Type $K3^{[2]}$ - this is the content of the second part of the paper.

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Kieran G. O'Grady. 2021-09-15. Moduli of sheaves on $K3$'s and higher dimensional HK varieties. https://arxiv.org/abs/2109.07425

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