Arithmetic degree and associated graded modules |
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Authors: | Natale Paolo Vinai |
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Institution: | (1) Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy |
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Abstract: | We prove that the arithmetic degree of a graded or local ring A is bounded above by the arithmetic degree of any of its associated graded rings with respect to ideal I in A. In particular, if Spec(A) is equidimensional and has an embedded component (i.e., A has an embedded associated prime ideal), then the normal cone of Spec(A) along V(I) has an embedded component too. This extends a result of W. M. Ruppert about embedded components of the tangent cone.Mathematics Subject Classification (2000): Primary 13H15, 13A30; Secondary 13D45, 14Q99 |
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