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On the mixed multiplicity and the multiplicity of blow-up rings of equimultiple ideals

✍ Scribed by Duong Quôc Viêt

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
194 KB
Volume
183
Category
Article
ISSN
0022-4049

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✦ Synopsis

Let (S; m) be a graded algebra of dimension d generated by ÿnitely many elements of degree 1 over a ÿeld k and a homogeneous equimultiple ideal I of S with htI = h ¿ 0: In this paper we will show that if a1 6 a2 6 • • • 6 a h is the degree sequence of a minimal homogeneous reduction of I , then the mixed multiplicity e(m [d-i] ; I [i] ) = a1a2 • • • aie(S) for all 0 ¡ i ¡ h and the multiplicity of Rees algebra e(R(I )) = [1 + h-1 i=1 a1a2 • • • ai]e(S).

📜 SIMILAR VOLUMES

Burch's inequality and the depth of the
Burch's inequality and the depth of the blow up rings of an ideal
✍ Teresa Cortadellas; Santiago Zarzuela 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 187 KB

Let (A; m) be a local noetherian ring with inÿnite residue ÿeld and I an ideal of A. Consider RA(I ) and GA(I ), respectively, the Rees algebra and the associated graded ring of I , and denote by l(I ) the analytic spread of I . Burch's inequality says that l(I )+inf {depth A=I n ; n ≥ 1} ≤ dim(A),