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

Ayse Altintas

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arXiv · 1202.4992

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

Ayse Altintas

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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.

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BibTeX RIS

Ayse Altintas. 2014-03-27. Examples of finitely determined map-germs of corank 2 from $n$-space to $(n+1)$-space. https://arxiv.org/abs/1202.4992

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