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/}
}
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/