Equisingularity of map germs from a surface to the plane

J. J. Nuño-Ballesteros; B. Oréfice-Okamoto; J. N. Tomazella

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arXiv · 1507.01483

Equisingularity of map germs from a surface to the plane

J. J. Nuño-Ballesteros·B. Oréfice-Okamoto·J. N. Tomazella

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Abstract

Let $(X,0)$ be an ICIS of dimension 2 and let $f:(X,0)\to (\C^2,0)$ be a map germ with an isolated instability. We look at the invariants that appear when $X_s$ is a smoothing of $(X,0)$ and $f_s:X_s\to B_\epsilon$ is a stabilization of $f$. We find relations between these invariants and also give necessary and sufficient conditions for a $1$-parameter family to be Whitney equisingular. As an application, we show that a family $(X_t,0)$ is Zariski equisingular if and only if it is Whitney equisingular and the numbers of cusps and double folds of a generic linear projection are constant on $t$.

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BibTeX RIS

J. J. Nuño-Ballesteros, B. Oréfice-Okamoto, J. N. Tomazella. 2015-07-06. Equisingularity of map germs from a surface to the plane. https://arxiv.org/abs/1507.01483

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