We consider a relative Fourier-Mukai transform defined on elliptic fibrations over an arbitrary normal base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah's and Tu's results about semistable sheaves over elliptic curves to the case of elliptic fibrations. Moreover we show that this transform preserves relative (semi)stability of sheaves of positive relative degree.
arXiv Mathematics e-prints
- Pub Date:
- September 2001
- Mathematics - Algebraic Geometry;
- 11 pages, Latex. v2 corrects an error in Proposition 2.9. The statement of the main theorem remains unaltered but the proof needs to be slightly modified