The invention relates to a method for forming curved cuts in a transparent material, in particular in the cornea, by the creation of optical perforations in said material using laser radiation that is focused in the material. The focal point is displaced three-dimensionally to form the cut by lining up the optical perforations. The focal point is displaced in a first spatial direction by a displaceable lens and said focal directions in such a way that it follows the contours of the cut, which lie on a plane that is substantially perpendicular to the first spatial direction.