A short proof of the length formula of Hoskin and Deligne

Abstract

We give a particularly short and elementary proof of the length formula of Hoskin and Deligne. Unlike Johnston and Verma (Math. Proc. Cambridge Philos. Soc. 111, 423-432 (1992)), we don't first prove a formula for the multiplicity of a complete m-primary ideal of a two-dimensional regular local ring (R, m).