Torus fibrations, gerbes, and duality
| dc.creator | Donagi, Ron | |
| dc.creator | Pantev, Tony | |
| dc.date | 2003-06-13 | |
| dc.date | 2004-11-30 | |
| dc.date.accessioned | 2026-07-07T04:58:57Z | |
| dc.date.available | 2026-07-07T04:58:57Z | |
| dc.description | Let X be a smooth elliptic fibration over a smooth base B. Under mild assumptions, we establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an O^* gerbe over a genus one fibration which is a twisted form of X. The roles of the gerbe and the twist are interchanged by our duality. We state a general conjecture extending this to allow singular fibers, and we 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. | |
| dc.description | 74 pages, LaTeX 2e, with an appendix by D.Arinkin, minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0306213 | |
| dc.identifier | http://arxiv.org/abs/math/0306213 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67790 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Differential Geometry | |
| dc.title | Torus fibrations, gerbes, and duality | |
| dc.type | text |