On a relative Fourier-Mukai transform on genus one fibrations
arXiv:math/0410349
Abstract
We study relative Fourier-Mukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and non-projective. Grothendieck duality is used to prove a skew-commutativity relation between this equivalence of categories and certain duality functors. We use our results to explicitly construct examples of semi-stable sheaves on degenerating families of elliptic curves.
Major revision, clearer notation, improved presentation, simplified proofs and new examples included; 27 pages