Книга: Deformation theory: Differential calculus, Physics, Geometry of numbers, Perturbation theory, Complex manifold, Algebraic variety, Kunihiko Kodaira, Donald ... Spencer, Zariski tangent space, Moduli space

In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions P?, where ? is a small number, or vector of small quantities. The infinitesimal conditions are therefore the result of applying the approach of differential calculus to solving a problem with constraints. One can think of a structure that is not completely rigid, and that deforms slightly to accommodate forces applied from outside this explains the name.Some characteristic phenomena are: the derivation of first-order equations by treating the ? quantities as having negligible squares the possibility of isolated solutions, in that varying a solution may not be possible, or does not bring anything new and the question of whether the infinitesimal constraints actually 'integrate', so that their solution does provide small variations. In some form these considerations have a history of centuries in mathematics, but also in physics and engineering.