Abstract
Let (X, 0) be an ICIS of dimension 2 and let \(f:(X,0)\rightarrow (\mathbb C^2,0)\) 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 \(f_s:X_s\rightarrow B_\epsilon \) 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 with respect to t.
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J. J. Nuño-Ballesteros is partially supported by DGICYT Grant MTM2015-64013-P and CAPES-PVE Grant 88881.062217/2014-01. B. Oréfice-Okamoto is partially supported by FAPESP Grant 2013/14014-3. J. N. Tomazella is partially supported by CNPq Grant 309626/2014-5 and FAPESP Grant 2016/04740-7.
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Nuño-Ballesteros, J.J., Oréfice-Okamoto, B. & Tomazella, J.N. Equisingularity of map germs from a surface to the plane. Collect. Math. 69, 65–81 (2018). https://doi.org/10.1007/s13348-017-0194-6
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DOI: https://doi.org/10.1007/s13348-017-0194-6