KASS seminar

Abstract: Given an ideal J_x\subset O_x generated by a tuple f of holomorphic functions at x\in \C^n with common zero set {x}, the classical King's formula asserts that the Lelong number at x of the Monge-Ampère product (dd^c \log |f|^2)^n is the Hilbert-Samuel multiplicity of J_x.

I will discuss a joint work in progress with Mats Andersson, Richard Lärkäng, and Rahim Nkunzimana where we generalize this result to modules. Given a submodule K_x\subset O_x^s such that O_x^s/K_x has support at x, we prove that the so-called Buchsbaum-Rim multiplicity of K_x can be represented as the Lelong number of a current constructed in terms of Monge-Ampère products of generators of K_x.