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

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

2012-02-22

arxiv.org/abs/1202.4992v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

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. In this paper, we give the first examples of finitely determined map-germs of corank 2 from 3-space to 4-space satisfying the conjecture. We introduce a method for generating series of finitely determined map-germs in dimensions $(n,n+1)$ from a given finitely determined map-germ in dimensions $(n-1,n)$. We present more examples in the dimensions $(4,5)$ and $(5,6)$, and verify the conjecture for them.

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