Open problems in deformations of Artinian algebras, Hilbert schemes and around

Abstract

We review the open problems in the theory of deformations of zero-dimensional objects, such as algebras, modules or tensors. We list both the well-known ones and some new ones that emerge from applications. In view of many advances in recent years, we can hope that all of them are in the range of current methods.

v2: small updates on the problems, some marked as solved