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arXiv · 1308.0582

Multiplicities of Classical Varieties

Jack Jeffries·Jonathan Montaño·Matteo Varbaro
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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.

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Jack Jeffries, Jonathan Montaño, Matteo Varbaro. 2014-12-17. Multiplicities of Classical Varieties. https://doi.org/10.1112/plms%2Fpdv005

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