Mateusz Michałek


k-regular maps - from topology to algebraic geometry and back again


k-regular maps were first introduced by Borsuk in the 1957, contributing to the theory of embeddings of topological manifolds. Since then, they were intensively studied by the topologists. In the first, shorter part of the talk we will provide all the definitions and briefly describe the latest, topological results.
In the second part of the talk we will report on the joint project with Jarosław Buczyński, Tadeusz Januszkiewicz and Joachim Jelisiejew. We relate k-regular maps to certain Gorenstein schemes and hence to the geometry of the Gorenstein locus of the punctual Hilbert scheme. Basing on algebraic results, we provide new insight into the topological theory.