Project without external funding

Computational Koszul Homology and Spencer Cohomology

Project Details
Project duration: 10/200610/2010

The project studies effective methods for the explicit determination of the Koszul homology of polynomial modules (or dually the Spencer cohomology of comodules). This is in principle equivalent to the computation of a minimal free resolution, however, it is still an open problem to find an explicit representation of the required isomorphism. We study various direct methods for the construction of the Koszul homology first of monomial modules and then of polynomial modules. In the monomial case we use different techniques of combinatorial, topological or algebraic origin. One possibility for an extension to the polynomial case is via homological perturbation theory. We are also interested in the precise relationship between Pommaret bases and the Koszul homology (or Spencer cohomology, resp.).

Principal Investigator

Research Areas

Last updated on 2017-11-07 at 14:54