Castelnuovo-Mumford regularity and extended degree

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 exten...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2003-05, Vol.355 (5), p.1773-1786
Main Authors: Rossi, Maria Evelina, Trung, Ngô Viêt, Valla, Giuseppe
Format: Article
Language:English
Subjects:
Algebra
Commutative rings and algebras
Cones
Exact sciences and technology
Geometry
Integers
Mathematical functions
Mathematical rings
Mathematical theorems
Mathematics
Polynomials
Sciences and techniques of general use
Tangents
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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.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-03-03185-4