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Funktsional. Anal. i Prilozhen., 2003, Volume 37, Issue 2, Pages 52–64 (Mi faa148)  

This article is cited in 10 scientific papers (total in 10 papers)

Resolution of Corank $1$ Singularities of a Generic Front

V. D. Sedykh

Gubkin Russian State University of Oil and Gas

Abstract: 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

DOI: https://doi.org/10.4213/faa148

Full text: PDF file (191 kB)
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English version:
Functional Analysis and Its Applications, 2003, 37:2, 123–133

Bibliographic databases:

UDC: 515.16
Received: 19.02.2002

Citation: V. D. Sedykh, “Resolution of Corank $1$ Singularities of a Generic Front”, Funktsional. Anal. i Prilozhen., 37:2 (2003), 52–64; Funct. Anal. Appl., 37:2 (2003), 123–133

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. D. Sedykh, “On the topology of singularities of Maxwell sets”, Mosc. Math. J., 3:3 (2003), 1097–1112  mathnet  crossref  mathscinet  zmath
    2. V. D. Sedykh, “On the topology of stable corank 1 singularities on the boundary of a connected component of the complement to a front”, Sb. Math., 195:8 (2004), 1165–1203  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. V. D. Sedykh, “A Complete System of Linear Relations between the Euler Characteristics of Manifolds of Corank $1$ Singularities of a Generic Front”, Funct. Anal. Appl., 38:4 (2004), 298–301  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Sedykh V.D., “On the topology of the image of a stable smooth mapping with singularities of corank 1”, Dokl. Math., 69:2 (2004), 235–239  mathnet  mathscinet  zmath  isi
    5. V. D. Sedykh, “Corank 1 Singularities of Stable Smooth Maps and Special Tangent Hyperplanes to a Space Curve”, Math. Notes, 78:3 (2005), 378–390  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. Sedykh V.D., “The topology of corank 1 multi-singularities of stable smooth mappings of equidimensional manifolds”, C. R. Math. Acad. Sci. Paris, 340:6 (2005), 441–444  crossref  mathscinet  zmath  isi  scopus
    7. Sedykh V.D., “On the topology of singularities of the set of supporting hyperplanes of a smooth submanifold in an affine space”, J. London Math. Soc. (2), 71:1 (2005), 259–272  crossref  mathscinet  zmath  isi  scopus
    8. V. D. Sedykh, “Resolution of corank 1 singularities in the image of a stable smooth map to a space of higher dimension”, Izv. Math., 71:2 (2007), 391–437  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. V. D. Sedykh, “On the topology of wave fronts in spaces of low dimension”, Izv. Math., 76:2 (2012), 375–418  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. V. D. Sedykh, “On Euler Characteristics of Manifolds of Singularities of Wave Fronts”, Funct. Anal. Appl., 46:1 (2012), 77–80  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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