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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Castelnuovo-Mumford regularity and extended degree


Authors: Maria Evelina Rossi, Ngô Viêt Trung and Giuseppe Valla
Journal: Trans. Amer. Math. Soc. 355 (2003), 1773-1786
MSC (2000): Primary 13A30, 13D45
Published electronically: January 13, 2003
MathSciNet review: 1953524
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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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Additional Information

Maria Evelina Rossi
Affiliation: Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16132 Genova, Italy
Email: rossim@dima.unige.it

Ngô Viêt Trung
Affiliation: Institute of Mathematics, Box 631, Bò Hô, 10000 Hanoi, Vietnam
Email: nvtrung@thevinh.ncst.ac.vn

Giuseppe Valla
Affiliation: Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16132 Genova, Italy
Email: valla@dima.unige.it

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03185-4
PII: S 0002-9947(03)03185-4
Received by editor(s): August 9, 2002
Published electronically: January 13, 2003
Additional Notes: The first and third authors are partially supported by MPI of Italy. The second author is partially supported by the National Basic Research Program of Vietnam
Article copyright: © Copyright 2003 American Mathematical Society