Geometry & Topology Seminar

Eric Boulter, Department of Pure Mathematics, University of Waterloo

"Smooth and Compact Moduli Spaces of Sheaves on Kodaira Surfaces"

Holomorphic symplectic manifolds are an important class of complex manifolds for the classification of manifolds with trivial first Chern class, as well as for several physics applications. However, it is notoriously difficult to find compact examples of holomorphic symplectic manifolds. In 2001, Toma proved a sufficient condition for a moduli space of coherent sheaves with fixed determinant bundle and Chern character over a Kodaira surface to be a compact holomorphic symplectic manifold. In this talk we show that moduli spaces satisfying Toma’s condition occur in all possible dimensions and analyze a natural fibration on these moduli spaces to partially determine their structure for moduli spaces with dimension at most 6. 

Zoom meeting: https://zoom.us/j/93859138328