Vector-tensor multiplet in N = 2 superspace with central charge

We use the four-dimensional N = 2 central charge superspace to give a geometrical construction of the Abelian vector-tensor multiplet consisting, under N = 1 supersymmetry, of one vector and one linear multiplet. We derive the component field supersymmetry and central charge transformations, and show that there is a super-Lagrangian, the higher components of which are all total derivatives, allowing us to construct superfield and component actions.