Gieseker Stability and the Fourier-Mukai Transform for Abelian Surfaces.

摘要

The preservation properties of Gieseker stability and semistability under the Fourier transform of Mukai are discussed. A fundamental lemma is proved describing the degree of sheaves whose Fourier transforms are concentrated in degrees 0 or 2. This is used to prove results about the behavior of both Gieseker stability and Mumford-Takemoto stability under the Fourier transform.