Abstract

This talk reports on joint work with Daniel Greb. Let X be a complex projective manifold, In order to obtain reasonable moduli spaces for algebraic vector bundles on X, Mumford introduced the notion of “slope-stability” when dim(X)=1. His definition was later extended to higher dimensions. For dim(X)>1 Giesecker and Maruyama considered a new stability notion which allowed them to construct also in this case moduli spaces of semistable sheaves. Later Le Potier and Li gave a construction when dim(X)=2 of moduli spaces of slope-semistable sheaves. These spaces are homeomorphic to the compactifications of moduli spaces of Yang-Mills connections obtained by Donaldson and Uhlenbeck in gauge theory. In this talk we present a construction of a moduli space of slope-semistable coherent sheaves in higher dimensions. We also explain the pathologies connected to change of polarization, which are encountered in this case.