Multiplicity of the special fiber of blowups

Corso, Alberto; Polini, Claudia; Vasconcelos, Wolmer V.

Multiplicity of the special fiber of blowups

Authors

Corso, Alberto

Polini, Claudia

Vasconcelos, Wolmer V.

Description

Let $(R, {\mathfrak m})$ be a Noetherian local ring and let $I$ be an ${\mathfrak m}$-primary ideal. In this paper we give sharp bounds on the multiplicity of the special fiber ring ${\mathcal F}$ 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 ${\mathcal F}$.
14 pages