On a relative Fourier-Mukai transform on genus one fibrations

Details On a relative Fourier-Mukai transform on genus one fibrations On a relative Fourier-Mukai transform on genus one fibrations

2004-10-15

arxiv.org/abs/math/0410349v2

Mathematics

Algebraic Geometry

Major revision, clearer notation, improved presentation, simplified proofs and new examples included; 27 pages

Scientific paper

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.

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