Examples of finitely determined map-germs of corank 2 from n-space to (n+1)-space

Abstract

We produce new examples supporting the Mond conjecture which can be stated as follows. The number of parameters needed for a miniversal unfolding of a finitely determined map-germ from n-space to (n + 1)-space is less than (or equal to if the map-germ is weighted homogeneous) the rank of the nth homology group of the image of a stable perturbation of the map-germ. We give examples of finitely determined map-germs of corank 2 from 3-space to 4-space satisfying the conjecture. We introduce a new type of augmentations to generate series of finitely determined map-germs in dimensions (n, n + 1) from a given one in dimensions (n - 1, n). We present more examples in dimensions (4, 5) and (5, 6) based on our examples, and verify the conjecture for them.