Algorithmic Computation of Flattenings and of Modular Deformations

This paper presents an algorithm for the computation of any jet of the flattening stratum of a module over a local algebra based on an obstruction theory for lifting flatness. It is applied to modular deformations of singular germs. Infinitesimal modular deformations of isolated complete intersection singularities are characterized as flattening strata of its first tangent cohomology. Some examples are discussed that indicate relations with moduli spaces of certain classes of singularities. Implementations are done in SINGULAR .