Relatively stable bundles over elliptic fibrations
Abstract
We consider a relative FourierMukai 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2001
 arXiv:
 arXiv:math/0109123
 Bibcode:
 2001math......9123B
 Keywords:

 Mathematics  Algebraic Geometry;
 14D20;
 14F05;
 14H60
 EPrint:
 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