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We investigate the dynamics of space-time filling five-branes wrapped oncurves in heterotic and orientifold Calabi-Yau compactifications. We firststudy the leading N=1 scalar potential on the infinite deformation space of thebrane-curve around a supersymmetric configuration. The higher order potentialis also determined by a brane superpotential which we compute for a subset oflight deformations. We argue that these deformations map to new complexstructure deformations of a non-Calabi-Yau manifold which is obtained byblowing up the brane-curve into a four-cycle and by replacing the brane bybackground fluxes. This translates the original brane-bulk system into aunifying geometrical formulation. Using this blow-up geometry we compute thecomplete set of open-closed Picard-Fuchs differential equations and identifythe brane superpotential at special points in the field space for five-branesin toric Calabi-Yau hypersurfaces. This has an interpretation in open mirrorsymmetry and enables us to list compact disk instanton invariants. As a firststep towards promoting the blow-up geometry to a supersymmetric heteroticbackground we propose a non-Kaehler SU(3) structure and an identification ofthe three-form flux.

Five-Brane Superpotentials, Blow-Up Geometries and SU(3) Structure Manifolds