pith. sign in

arxiv: 1202.4992 · v3 · pith:XWFMLSW2new · submitted 2012-02-22 · 🧮 math.AG

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

classification 🧮 math.AG
keywords spaceexamplesdeterminedfinitelyconjecturedimensionsmap-germmap-germs
0
0 comments X
read the original 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 $n$th 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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.