Ana Bravo
On the multiplicity of embedded hypersurfaces
Let X be a hypersurface embedded in a smooth scheme W over field K. Then
the multiplicity of the hypersurface defines an upper-semi-continuous
function along the points of X, and hence the set of points of maximal
multiplicity of X is a closed set. This closed set can be described by
means of the so-called Tschirnhausen transformation, or by using
Hironaka's notion of maximal contact, whenever K is a field of
characteristic zero. We will present an alternative way of describing
this closed set.