IUMJ

Title: On the Hilbert-Samuel multiplicity of Fredholm tuples

Authors: Joerg Eschmeier

Issue: Volume 56 (2007), Issue 3, 1463-1478

Abstract:

For commuting tuples $R \in L(Z)^n$ of Banach-space operators that arise as quotients of lower semi-Fredholm systems $T$ with constant cohomology dimension $\dim H^n(z-T, X)$ near the origin $0 \in \mathbb{C}^n$, we show that the Hilbert-Samuel multiplicity of $R$ calculates the rank of the cohomology sheaf $\mathcal{H}^n(z-R, \mathcal{O}^Z_{\mathbb{C}^n})$ at $z = 0$.