Castelnuovo-Mumford regularity and extended degree
arXiv:math/0211178
Abstract
The main result of this paper shows that the Castelnuovo-Mumford regularity of the tangent cone of a local ring is effectively bounded by the dimension and any extended degree. From this it follows that there are only a finite number of Hilbert-Samuel functions of local rings with given dimension and extended degree.
15 pages