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Arithmetic degree and associated graded modules

Natale Paolo Vinai
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Abstract

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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Natale Paolo Vinai. 2004-02-27. Arithmetic degree and associated graded modules. https://arxiv.org/abs/math/0402455

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