Degree bounds for generators of cohomology modules and castelnuovo-mumford regularity

By extending Mumford's result on the generating by global sections there are estimates on the degree for generators of local cohomology modules. These arguments provide bounds on the Castelnuovo-Mumford regularity, in particular for Cohen-Macaulay varieties. As an application they imply a few more cases of varieties that satisfy a conjecture posed by Eisenbud and Gôto.