English

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

Algebraic Geometry 2014-03-28 v3

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 nn-space to (n+1)(n+1)-space is less than (or equal to if the map-germ is weighted homogeneous) the rank of the nnth 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)(n,n+1) from a given one in dimensions (n1,n)(n-1,n). We present more examples in dimensions (4,5)(4,5) and (5,6)(5,6) based on our examples, and verify the conjecture for them.

Keywords

Cite

@article{arxiv.1202.4992,
  title  = {Examples of finitely determined map-germs of corank 2 from $n$-space to $(n+1)$-space},
  author = {Ayse Altintas},
  journal= {arXiv preprint arXiv:1202.4992},
  year   = {2014}
}

Comments

v3: final version, to appear in International Journal of Mathematics. -- v2: 14 pages, shortened and revised: section on map-germs from 3-space to 4-space removed, the examples kept; remark 4.11 corrected, now it is remark 4.4; remark 4.12 revised; replaced the term 'reduction' with 'augmentation'