Mr Peter-Simon Dieterich (Universität Hamburg)
We formulate a correspondence between affine and projective special Kähler manifolds of the same dimension. As an application, we show that, under this correspondence, the affine special Kähler manifolds in the image of the rigid r-map are mapped to one-parameter deformations of projective special Kähler manifolds in the image of the supergravity r-map. The above one-parameter deformations are interpreted as perturbative $\alpha'$-corrections in heterotic and type-II string compactifications with $N=2$ supersymmetry. We show that the completeness of the deformed supergravity r-map metric depends solely on the (well-understood) completeness of the undeformed metric and the sign of the deformation parameter.
Mr Peter-Simon Dieterich (Universität Hamburg) Prof. Thomas Mohaupt (University of Liverpool) Prof. Vicente Cortés (Department of Mathematics, University of Hamburg)