Global residue currents and the Ext functors

Abstract

This thesis concerns developments in multivariable residue theory. In particular we consider global constructions of residue currents related to work by Andersson and Wulcan. In the first paper of this thesis, we consider global residue currents defined on projective space, and we show that these currents provide a tool for studying polynomial interpolation. Polynomial interpolation is related to local cohomology, and by a result known as local duality, there is a close connection with certain Ext groups. The second paper of this thesis is devoted to further study of connections between residue currents and the Ext functors. The main result is that we construct a global residue current on a complex manifold, and using this we give an explicit formula for an isomorphism of two different representations of the global Ext groups on complex manifolds.