2013-05-142013-05-142006Burban, I. and Kreussler, B. (2006) ‘On a relative Fourier-Mukai transform on genus one fibrations’, manuscripta mathematica 120, 283-306.http://hdl.handle.net/10395/1884We 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.engCopyright © Springer, Manuscripta Mathematica. This Publication can be obtained at http://www.springer.com/mathematics/journal/229MathematicsGenus One FibrationsRelative Fourier-Mukai transformsArticle