Surveys in Differential Geometry

Volume 24 (2019)

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

Pages: 403 – 440

DOI: https://dx.doi.org/10.4310/SDG.2019.v24.n1.a9

Author

Kieran G. O’Grady (Dipartimento di Matematica, Sapienza Università di Roma, Italy)

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 $K3^{[n]}$ (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 hyperkähler varieties of Type $K3^{[2]}$ — this is the content of the second part of the paper.

Published 29 December 2021