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• Författare:

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• Författare:

## Ron Donagi

• Förlag:

### Amer Mathematical Society

• Serie: Memoirs of the American Mathematical Society
• Bandtyp: Pocket
• Språk: Engelska
• Utgiven: 200804
• Antal sidor: 90
• Vikt i gram: 172
•  ISBN10: 0821840924
•  ISBN13: 9780821840924

# Torus Fibrations, Gerbes, and Duality

(Pocket)
av

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## Ron Donagi

##### Beskrivning:

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.