Fourier-Mukai Transform and Mirror Symmetry for D-Branes on Elliptic Calabi-Yau

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dc.creatorAndreas, Bjorn
dc.creatorCurio, Gottfried
dc.creatorRuiperez, Daniel Hernandez
dc.creatorYau, Shing-Tung
dc.date2000-12-20
dc.date.accessioned2026-07-07T04:39:20Z
dc.date.available2026-07-07T04:39:20Z
dc.descriptionFibrewise T-duality (Fourier-Mukai transform) for D-branes on an elliptic Calabi-Yau three-fold $X$ is seen to have an expected adiabatic form for its induced cohomology operation only when an appropriately twisted operation resp. twisted charge is defined. Some differences with the case of $K3$ as well as connections with the spectral cover construction for bundles on $X$ are pointed out. In the context of mirror symmetry Kontsevich's association of line bundle twists (resp. a certain 'diagonal' operation) with monodromies (esp. the conifold monodromy) is made explicit and checked for two example models. Interpreting this association as a relation between FM transforms and monodromies, we express the fibrewise FM transform through known monodromies. The operation of fibrewise duality as well as the notion of a certain index relevant to the computation of the moduli space of the bundle is transported to the sLag side. Finally the moduli space for D4-branes and its behaviour under the FM transform is considered with an application to the spectral cover.
dc.description47p, harvmac
dc.identifierhttps://arxiv.org/abs/math/0012196
dc.identifierhttp://arxiv.org/abs/math/0012196
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60619
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.titleFourier-Mukai Transform and Mirror Symmetry for D-Branes on Elliptic Calabi-Yau
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