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Classical Deformation Theory is used for determining the completions of local rings of an eventual moduli space. When a moduli variety exists, the main result explored in the book is that the local ring in a closed point can be explicitly computed as an algebraization of the pro-representing hull, called the local formal moduli, of the deformation functor for the corresponding closed point.The book gives explicit computational methods and includes the most necessary prerequisites for understanding associative algebraic geometry. It focuses on the meaning and the place of deformation theory,...

Deformation theory is used as a tool for studying the structure of moduli schemes in geometry by many mathematicians and physicists. Mainly, the structure of the obstruction groups and their vanishing is used for smoothness properties, but there is a need to find the structure of the singularities in moduli spaces as well. This can only be achieved by constructing the singularities, and this can be done by the deformation theory studied in this book, in particular in the study of liftings by generalized matric Massey products.