Noncommutative 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.