The Geometry of Double Fold Maps

Journal of Singularities
volume 10 (2014), 250-263

Received 29 January 2013. Received in revised form 21 February 2014.

DOI: 10.5427/jsing.2014.10q

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Abstract:

We study the geometry of a family of singular map germs (C^2,0)->(C^3,0) called double folds. As an analogy to David Mond's fold map germs of the form f(x,y)= (x, y^2, f_3(x,y)), f_3 in O_2, double folds are of the form f(x,y)=(x^2, y^2, f_3(x,y)). This family provides lots of interesting germs, such as finitely determined homogeneous corank 2 germs. We also introduce analytic invariants adapted to this family.

Author(s) information:

G. Peñafort-Sanchis