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Hermitian-Einstein connections on universal bundles

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Nicolas Addington
Thu, 13/04/2023 - 10:30 - 12:00
MPIM Lecture Hall

For a smooth, compact moduli space of stable vector bundles on a K3 surface, we construct a Hermitian-Einstein connection on the universal bundle, which restricts to a H-E connection on its "wrong-way" slices. Thus not only does the moduli space parametrize stable bundles on the K3 surface, but the K3 surface parametrizes stable bundles on the moduli space. Ingredients include the Bismut-Freed-Quillen connection on a determinant line bundle, and a careful analysis of the curvature of a certain principal bundle coming from gauge theory. This is joint work with Andrew Wray.

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