Moduli Spaces of Hermite-Einstein Connections over K3 Surfaces

dc.contributor.advisor	Addington, Nicolas
dc.contributor.author	Wray, Andrew
dc.date.accessioned	2020-09-24T17:17:28Z
dc.date.available	2020-09-24T17:17:28Z
dc.date.issued	2020-09-24
dc.description.abstract	We 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_US
dc.identifier.uri	https://hdl.handle.net/1794/25645
dc.language.iso	en_US
dc.publisher	University of Oregon
dc.rights	All Rights Reserved.
dc.subject	algebraic geometry	en_US
dc.subject	complex geometry	en_US
dc.subject	Hermite-Einstein metrics	en_US
dc.subject	K3 surfaces	en_US
dc.title	Moduli Spaces of Hermite-Einstein Connections over K3 Surfaces
dc.type	Electronic Thesis or Dissertation
thesis.degree.discipline	Department of Mathematics
thesis.degree.grantor	University of Oregon
thesis.degree.level	doctoral
thesis.degree.name	Ph.D.

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