Monomial equimultiple curves in positive characteristic

Abstract

It is known that the local equimultiple locus of a hypersurface in characteristic zero is contained in a regular hypersurface. Here we give an example of a monomial curve on a threefold in positive characteristic p > 2 p{\text { > }}2 which is equimultiple but not hyperplanar. As a corollary we have that any monomial curve which lies on a certain type of hypersurface (whose local equation is of a special form in its natural p p -basis expression) is automatically equimultiple for the hypersurface.