Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-06T01:11:48.410Z Has data issue: false hasContentIssue false

Multiplicity of the special fiber of blowups

Published online by Cambridge University Press:  22 February 2006

ALBERTO CORSO
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, U.S.A. e-mail: [email protected]
CLAUDIA POLINI
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, U.S.A. e-mail: [email protected]
WOLMER V. VASCONCELOS
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854, U.S.A. e-mail: [email protected]

Abstract

Let $(R, {\frak m})$ be a local Cohen–Macaulay ring and let $I$ be an ${\frak m}$-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 $I$. 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 ${\mathcal F}$.

Type
Research Article
Copyright
2006 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)