Multiplicity of the special fiber of blowups

DOI10.1017/S0305004105009023zbMATH Open1098.13030arXivmath/0307037OpenAlexW2171518868MaRDI QIDQ3377464

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Publication date: 22 March 2006

Published in: (Search for Journal in Brave)

Abstract: Let $(R,mathfrakm)$ be a Noetherian local ring and let $I$ be an $mathfrakm$-primary ideal. In this paper we give sharp bounds on the multiplicity of the special fiber ring $mathcalF$ of $I$ in terms of other well-known invariants of $I$. A special attention is then paid in studying when equality holds in these bounds, with a particular interest in the unmixedness or, better, the Cohen-Macaulayness of $mathcalF$.

Full work available at URL: https://arxiv.org/abs/math/0307037

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