Abstract

We introduce the technique of tracking numbers of graded algebras and modules. It is a modified version of the first Chern class of its free resolution relative to any of its standard Noether normalizations. Several estimations are obtained which are used to bound the length of chains of algebras occurring in the construction of the integral closure of a graded domain. Noteworthy is a quadratic bound on the multiplicity for all chains of algebras that satisfy the condition S2 of Serre.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 697-708
Launched on MUSE
2005-06-08
Open Access
No
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