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

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 hyperkähler variety of Type $K{3}^{[n]}$ (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 hyperkähler varieties of Type $K{3}^{[2]}$ - this is the content of the second part of the paper.

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

References in corpus (1)

• A Master Space for Moduli Spaces of Gieseker-Stable Sheaves