Moduli Spaces of Hermite-Einstein Connections over K3 Surfaces
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Date
2020-09-24
Authors
Wray, Andrew
Journal Title
Journal ISSN
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Publisher
University of Oregon
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.
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Keywords
algebraic geometry, complex geometry, Hermite-Einstein metrics, K3 surfaces