FoCM 2014 conference

Workshop C1 - Computational Algebraic Geometry

No date set

## Multiplicities of Classical Varieties

### Jack Jeffries

### University of Utah, United States - jeffries@math.utah.edu

The $j$-multiplicity plays an important role in the intersection theory of Stückrad-Vogel cycles, while recent developments confirm the connections between the $\epsilon$-multiplicity and equisingularity theory. 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 $\epsilon$-multiplicity of ideals defining determinantal varieties: The found quantities are integrals which, quite surprisingly, are central in random matrix theory. This is joint work with Jonathan Montaño and Matteo Varbaro.

Joint work with Jonathan Montaño (Purdue University, USA) and Matteo Varbaro (University of Genoa, Italy).