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.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/5285