A method and a device for processing a light-polymerizable material (5, 55) for building up an object (27) in layers, using a lithography based generative manufacture having a construction platform (12) for building up the object (27), a projecting exposure unit (10, 60) that can be controlled for locally selected exposing of a surface on the construction platform (12, 62) to an intensity pattern having a prescribed shape, and a control unit (11, 61) prepared for polymerizing overlapping layers (28) on the construction platform (12, 62) in successive exposure steps, each having a prescribed geometry, by controlling the projecting exposure unit (10, 60), in order to thus successively build up the object (27) in the desired shape, said shape resulting from the sequence of layer geometries. The invention is characterized in that a further exposure unit (16, 66) for exposing the surface of the construction platform (12, 62) is provided on the side opposite the projecting exposure unit (10, 60), and that the construction platform (12, 62) is designed to be at least partially transparent to light, and that the control unit (11, 61) is designed for controlling the further exposure unit (16, 66) at least while building up the first layer (28), said layer adhering to the construction platform (12, 62), for exposing in the prescribed geometry.