Castelnuovo-Mumford regularity and extended degree

Rossi, Maria Evelina; Trung, Ngô; Valla, Giuseppe

doi:10.1090/S0002-9947-03-03185-4

Castelnuovo-Mumford regularity and extended degree
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by Maria Evelina Rossi, Ngô Viêt Trung and Giuseppe Valla

Trans. Amer. Math. Soc. 355 (2003), 1773-1786

DOI: https://doi.org/10.1090/S0002-9947-03-03185-4

Published electronically: January 13, 2003

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Abstract:

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.

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