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Item Details
Title: TORUS FIBRATIONS, GERBES, AND DUALITY
By: Ron Donagi, Tony Pantev
Format: Paperback

List price: £67.50


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ISBN 10: 0821840924
ISBN 13: 9780821840924
Publisher: AMERICAN MATHEMATICAL SOCIETY
Pub. date: 15 April, 2008
Series: Memoirs of the American Mathematical Society 193, 901
Pages: 90
Description: Let $X$ be a smooth elliptic fibration over a smooth base $B$. Under mild assumptions, the authors establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an $\mathcal{O}^{\times}$ gerbe over a genus one fibration which is a twisted form of $X$.
Synopsis: Let $X$ be a smooth elliptic fibration over a smooth base $B$. Under mild assumptions, the authors establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an $\mathcal{O}{\times}$ gerbe over a genus one fibration which is a twisted form of $X$. The roles of the gerbe and the twist are interchanged by the authors' duality. The authors state a general conjecture extending this to allow singular fibers, and they prove the conjecture when $X$ is a surface. The duality extends to an action of the full modular group. This duality is related to the Strominger-Yau-Zaslow version of mirror symmetry, to twisted sheaves, and to non-commutative geometry.
Publication: US
Imprint: American Mathematical Society
Returns: Returnable
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