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On a relative Fourier-Mukai transform on genus one fibrations

Igor Burban·Bernd Kreussler
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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.

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Igor Burban, Bernd Kreussler. 2005-06-14. On a relative Fourier-Mukai transform on genus one fibrations. https://arxiv.org/abs/math/0410349

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