Castelnuovo–Mumford regularity

Summary

The Castelnuovo–Mumford regularity is an integer that bounds the degrees in the minimal free resolution of a finitely generated graded module over a polynomial ring. It measures how complicated the module is from the point of view of syzygies. It bounds the degree from which the Hilbert function agrees with the Hilbert polynomial. It also bounds the complexity of Gröbner basis computations.