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Algebraic Geometry Seminar

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
347 Altgeld Hall
Date
Nov 8, 2022   3:00 pm  
Speaker
Nicolas Addington, University of Oregon
Contact
Sheldon Katz
Views
79

Hermitian-Einstein connections on universal bundles

Abstract: 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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