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

Kieran G. O'Grady

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

Algebraic Geometry 2021-09-16 v1

Authors: Kieran G. O'Grady

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.

Keywords

moduli of sheaves k3 surfaces hyperkähler varieties chern character vector bundles stable sheaves

Cite

@article{arxiv.2109.07425,
  title  = {Moduli of sheaves on $K3$'s and higher dimensional HK varieties},
  author = {Kieran G. O'Grady},
  journal= {arXiv preprint arXiv:2109.07425},
  year   = {2021}
}

Comments

Dedicated to Shing-Tung Yau on the occasion of his 70th birthday. arXiv admin note: text overlap with arXiv:1912.02659

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

Abstract

Keywords

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