Geodesic
Resolution of Corank $1$ Singularities of a Generic Front
Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 2, pp. 52-64

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We construct a resolution of singularities for wave fronts having only stable singularities of corank $1$. It is based on a transformation that takes a given front to a new front with singularities of the same type in a space of smaller dimension. This transformation is defined by the class $A_{\mu}$ of Legendre singularities. The front and the ambient space obtained by the $A_{\mu}$-transformation inherit topological information on the closure of the manifold of singularities $A_{\mu}$ of the original front. The resolution of every (reducible) singularity of a front is determined by a suitable iteration of $A_{\mu}$-transformations. As a corollary, we obtain new conditions for the coexistence of singularities of generic fronts.
Keywords: Legendre mapping, wave front, stable corank $1$ singularity, resolution of singularities, Euler number. 
@article{FAA_2003_37_2_a5,
     author = {V. D. Sedykh},
     title = {Resolution of {Corank} $1$ {Singularities} of a {Generic} {Front}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {52--64},
     publisher = {mathdoc},
     volume = {37},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2003_37_2_a5/}
}
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V. D. Sedykh. Resolution of Corank $1$ Singularities of a Generic Front. Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 2, pp. 52-64. http://geodesic.mathdoc.fr/item/FAA_2003_37_2_a5/