Group actions on moduli of vector bundles.

Abstract

In this thesis we study the action of the group of projective transformations on suitable moduli spaces of sheaves on projective spaces and try to understand the semistable points in the sense of Mumford's geometric invariant theory. For sheaves on the projective plane a very strong parallel is observed with the results, that were obtained by Mumford, of the corresponding action on the parameter space of curves of a fixed degree in the projective plane. On higher dimensional projective spaces we derive semistability conditions for classes of sheaves that get well described by linear algebraic data, among which are the very interesting classes of Steiner, Logarithmic, Schwarzenberger sheaves, and Mathematical Instantons.