On a Relative Fourier–Mukai Transform on Genus One Fibrations |
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Authors: | Igor Burban Bernd Kreußler |
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Institution: | (1) Fachbereich Physik, Mathematik und Informatik, Institut für Mathematik, Johannes-Gutenberg Universität Mainz, 55099 Mainz, Germany;(2) Mary Immaculate College, South Circular Road, Limerick, Ireland |
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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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Keywords: | 18E30 14H60 14H20 14J27 14H10 |
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