ABSTRACT
Some time ago the first author conjectured (in [9]) that every A e https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203912089/10e95e2c-eca6-48d5-adf5-58298374b4f7/content/eq2385.tif"/> -codimension 1 equivalence class of map-germs ( ℂ n , S ) → ( ℂ p , 0 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203912089/10e95e2c-eca6-48d5-adf5-58298374b4f7/content/eq2386.tif"/> , with n ≥ p − 1 and (n, p) nice dimensions, should have a real form with a “good real perturbation” — that is, the A https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203912089/10e95e2c-eca6-48d5-adf5-58298374b4f7/content/eq2387.tif"/> -equivalence class should contain a real germ (one whose power-series expansion has purely real coefficients) which moreover should have a real perturbation whose real discriminant (if n ≥ p) or real image (if n = p − 1) carries the vanishing homology of its complexification. The purpose of this note is to give an example for which this does not hold — thus proving the conjecture false.
