Addington, NicolasWray, Andrew2020-09-242020-09-242020-09-24https://hdl.handle.net/1794/25645We study the moduli space M of twisted Hermite-Einstein connections on a vector bundle over a K3 surface X. We show that the universal bundle can be viewed as a family of stable vector bundles over M parameterized by X, therefore identifying X with a component of a moduli space of sheaves over M. The proof hinges on a new realization of twisted differential geometry that puts untwisted and twisted bundles on equal footing. Moreover, we use this technique to give a new and streamlined proof that M is nonempty, compact, and deformation-equivalent to a Hilbert scheme of points on a K3 surface, and that the Mukai map is a Hodge isometry.en-USAll Rights Reserved.algebraic geometrycomplex geometryHermite-Einstein metricsK3 surfacesElectronic Thesis or Dissertation