Relatively stable bundles over elliptic fibrations

Details Relatively stable bundles over elliptic fibrations Relatively stable bundles over elliptic fibrations

2001-09-18

arxiv.org/abs/math/0109123v2

Math. Nach. 238 (2002) 23-36

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 ne

Scientific paper

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.

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