Arithmetic degree and associated graded modules

Natale Paolo Vinai

Arithmetic degree and associated graded modules

Commutative Algebra 2007-05-23 v1 Algebraic Geometry

Authors: Natale Paolo Vinai

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.

Keywords

commutative algebra monomial ideals module theory

Cite

@article{arxiv.math/0402455,
  title  = {Arithmetic degree and associated graded modules},
  author = {Natale Paolo Vinai},
  journal= {arXiv preprint arXiv:math/0402455},
  year   = {2007}
}

Comments

13 pages

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