Arithmetic degree and associated graded modules

Details Arithmetic degree and associated graded modules Arithmetic degree and associated graded modules

2004-02-27

arxiv.org/abs/math/0402455v1

Mathematics

Commutative Algebra

13 pages

Scientific paper

We prove that the arithmetic degree of a graded or local ring is bounded
above by the arithmetic degree of any of its associated graded rings with
respect to ideals $I$ in $A$. In particular, if $Spec (A)$ is equidimensional
and has an embedded component in dimension $i$, then the normal cone of $Spec
(A)$ along $V(I)$ has an embedded component in dimension $i$ too.

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