ABSTRACT. The j-multiplicity plays an important role in the intersection theory of Stückrad-Vogel cycles, while recent developments confirm the connections between the ε-multiplicity and equisingularity theory. In this paper we establish, under some constraints, a relationship between the j-multiplicity of an ideal and the degree of its fiber cone. As a consequence, we are able to compute the j-multiplicity of all the ideals defining rational normal scrolls. By using the standard monomial theory, we can also compute the j-and ε-multiplicity of ideals defining determinantal varieties: The found quantities are integrals which, quite surprisingly, are central in random matrix theory.
One can also compute ǫ(I) for determinantal ideals using some integrals that arise in random matrix theory, see REF .
Multiplicities of Classical Varieties
Mathematics