A framework was developed in a joint work with F. J. Gallego and M. Gonzalez to systematically deal with the deformation of finite morphisms, multiple scheme structures on algebraic varieties and their smoothing. There are several applications of this framework. In this talk I will talk about some of them. First is the description of some components of the moduli space of varieties of general type in all dimensions. In particular, we show the existence of components of the moduli space of general type in all dimensions that are analogue of the moduli space of curves of genus g≥2�≥2. Secondly, we give a new method to construct smooth varieties in projective space embedded by complete sub canonical linear series within the range of the Hartshorne conjecture and beyond. Are all of them complete intersections? We also construct systematically, smooth non complete intersection subvarieties embedded by complete linear series outside the range of the Hartshorne conjecture. As a byproduct, we construct simple canonical varieties of any dimension, expanding the original question posed by Enriques for algebraic surfaces. This is joint work with F. J. Gallego, J. Mukherjee and D. Raychaudhury.