Torus Fibrations, Gerbes, and Duality
Seiten
2008
American Mathematical Society (Verlag)
978-0-8218-4092-4 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-4092-4 (ISBN)
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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 $X$.
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.
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.
Introduction The Brauer group and the Tate-Shafarevich group Smooth genus one fibrations Surfaces Modified $T$-duality and the SYZ conjecture Appendix A. Duality for representations of $1$-motives, by Dmitry Arinkin Bibliography.
| Erscheint lt. Verlag | 1.6.2008 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-8218-4092-4 / 0821840924 |
| ISBN-13 | 978-0-8218-4092-4 / 9780821840924 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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