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We discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram.
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1971
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1978
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Bernard Teissier, Appendix to : O. Zariski, Le problème des modules pour les branches planes. Course given at the Centre de Mathématiques de l’Ecole Polytechnique, Paris, October–November 1973. Second edition. Hermann, Paris, 1986
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Ignacio Luengo, The μ \mu -constant stratum is not smooth
1987
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Ignacio Luengo, On the Existence of Complete Families of Projective Plane Curves, which are Obstructed
1987
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V. I. Arnol’d, S. M. Guseĭn-Zade and A. N. Varchenko, Singularities of differentiable maps. Volume II: Monodromy and asymptotics of integrals
1988
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Ruud Pellikaan, Finite determinacy of functions with non-isolated singularities
1988
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Jan Denef and Kathleen Hoornaert, Newton Polyhedra and Igusa’s Local Zeta Function
2000
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A. Melle-Hernández and C. T. C. Wall, Pencils of curves on smooth surfaces
2001
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Vladimir I. Arnold (ed), Arnold’s Problems
2005
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Andrew A. du Plessis, Minimal Intransigent Hypersurfaces
2006
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Angel Montesinos, Gérmenes
2009
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Yousra Boubakri, Gert-Martin Greuel and Thomas Markwig, Invariants of hypersurface singularities in positive characteristic
2012
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Jan Stevens, On the μ \mu -constant stratum and the V V -filtration: an example
1989
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P. Cassou-Noguès, Courbes de semi-groupe donné
1991
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Theo de Jong and Duco van Straten, On the base space of a semi-universal deformation of rational quadruple points
1991
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C.T.C. Wall, Newton polytopes and non-degeneracy
1999
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Peter Beelen and Ruud Pellikaan, The Newton Polygon of Plane Curves with Many Rational Points
2000
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Cited in the paper.
Gert-Martin Greuel and Hong Duc Nguyen, Some remarks on the planar Kouchnirenko’s theorem
2012
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G. Oleksik The Łojasiewicz exponent of nondegenerate surface singularities
2013
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Szymon Brzostowski, Tadeusz Krasiński and Justyna Walewska, Arnold’s problem on monotonicity of the Newton number for surface singularities
2019
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W. Decker, G.-M. Greuel, G. Pfister and H. Schönemann. Singular
2019
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