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Castelnuovo-Mumford regularity and extended degree. (English) Zbl 1075.13008
Summary: Our main result shows that the Castelnuovo-Mumford regularity of the tangent cone of a local ring \(A\) is effectively bounded by the dimension and any extended degree of \(A\). From this it follows that there are only a finite number of Hilbert-Samuel functions of local rings with given dimension and extended degree.

MSC:
13D45 Local cohomology and commutative rings
13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
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