Seminário de Geometria
Title: Hyperholomorphic sheaves
Abstract: A hyperkahler manifold is a Riemannian manifold equipped
with an action of quaternion algebra in its tangent bundle
which is parallel with respect to the Levi-Civita connection.
A vector bundle with connection on a hyperkahler manifold
is called hypercolomorphic if its curvature is invariant
under the quaternion action. Such connections can be
obtained by applying the Kobayashi-Hitchin correspondence
(the correspondence between the stable bundles and the
instantons) to stable bundles with quaternionic invariant
Chern classes c1 and c2. I will give an overview
of this construction and explain how to extend this
correspondence to coherent sheaves by considering the
singular solutions of the instanton equation.