In mathematics, the Koszul cohomology groups are groups associated to a projective variety X with a line bundle L. They were introduced by , and named after Jean-Louis Koszul as they are closely related to the Koszul complex.
surveys early work on Koszul cohomology, gives an introduction to Koszul cohomology, and gives a more advanced survey.
If M is a graded module over the symmetric algebra of a vector space V, then the Koszul cohomology of M is the cohomology of the sequence
If L is a line bundle over a projective variety X, then the Koszul cohomology is given by the Koszul cohomology of the graded module , viewed as a module over the symmetric algebra of the vector space .