A layer construction method for the additive manufacture of at least one component region of a component, comprising at least the following steps: a) applying at least one powder layer of a metallic and/or intermetallic material to at least one build-up and joining zone (I) of at least one lowerable construction platform ; b) layer-wise and local melting and/or sintering of the material to form a component layer by selective exposure of the material with at least one high-energy beam in accordance with a predetermined exposure strategy; c) layered lowering of the construction platform by a predefined layer thickness; and d) repeating steps a) through d) until completion of the component region, wherein during the manufacture of the component region - at least one component layer is heated; - at least one image of the component layer is acquired by means of a camera system , the image characterizing a temperature distribution of the component layer ; and - a check for the presence of at least one near-surface defect from the group of cracks, binding defects, inclusions and other defects in the component layer being carried out by means of a computing device on the basis of the at least one acquired image, characterized in that the at least one component layer is heated by generating eddy currents in the component layer by applying electrical current to at least one induction coil and moving it relative to the component layer , the mean relative speed between the induction coil and the component layer being between 1 mm/s and 250 mm/s. a) applying at least one powder layer of a metallic and/or intermetallic material to at least one build-up and joining zone (I) of at least one lowerable construction platform ; b) layer-wise and local melting and/or sintering of the material to form a component layer by selective exposure of the material with at least one high-energy beam in accordance with a predetermined exposure strategy; c) layered lowering of the construction platform by a predefined layer thickness; and d) repeating steps a) through d) until completion of the component region, wherein during the manufacture of the component region - at least one component layer is heated; - at least one image of the component layer is acquired by means of a camera system , the image characterizing a temperature distribution of the component layer ; and - a check for the presence of at least one near-surface defect from the group of cracks, binding defects, inclusions and other defects in the component layer being carried out by means of a computing device on the basis of the at least one acquired image, characterized in that the at least one component layer is heated by generating eddy currents in the component layer by applying electrical current to at least one induction coil and moving it relative to the component layer , the mean relative speed between the induction coil and the component layer being between 1 mm/s and 250 mm/s. - at least one component layer is heated; - at least one image of the component layer is acquired by means of a camera system , the image characterizing a temperature distribution of the component layer ; and - a check for the presence of at least one near-surface defect from the group of cracks, binding defects, inclusions and other defects in the component layer being carried out by means of a computing device on the basis of the at least one acquired image, characterized in that the at least one component layer is heated by generating eddy currents in the component layer by applying electrical current to at least one induction coil and moving it relative to the component layer , the mean relative speed between the induction coil and the component layer being between 1 mm/s and 250 mm/s. <EOS>