Computations and stability of the Fukui invariant (Q2781942)

The Fukui invariant \(A(f)\) of the blow-analytic equivalence class of the analytic singularity \(f:K^n,0\to K,0\) (\(K=\mathbb{R}\) or \(\mathbb{C}\)) is defined as follows: take all analytic curves \(\lambda\) through 0 in \(K^n\) and consider the set \(A(f)=\{\)orders of \(f(\lambda(t))\}\). Fukui used toric resolutions to find formulae for \(A(f)\). NEWLINENEWLINENEWLINEIn the paper under review more general formulae are proved, using Hironaka-Bierstone-Milman desingularization techniques (for \(f\) being real or complex, degenerate or not). Using this new formula the authors define and characterize various notions of stability (stably periodic, stably interval-like) as well as define a sign of the Fukui invariant in the real case. If \(n=2\) they study how the so called tree-model of \(f\) determines \(A(f)\).