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

List price:
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£67.50 |
We currently do not stock this item, please contact the publisher directly for
further information.
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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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