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Simple singularities of space curves

  • C. G. Gibson (a1) and C. A. Hobbs (a1)
Abstract

The genesis of this paper lies in theoretical questions in kinematics where a central role is played by naturally occurring families of rigid motions of 3-space. The resulting trajectories are parametrized families of space curves, and it is important to understand the generic singularities they can exhibit. For practical purposes one seeks to classify germs of space curves of fairly small Ae-codimension. It is however little harder to list the A-simple germs, which includes all germs of Ae-codimension ≤11: that then is the principal objective of this paper.

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[3]J. W. Bruce , T. J. Gaffney and A. A. Du Plessis . On left equivalence of map germs. Bull. London Math. Soc. 16 (1984), 303306.

[4]J. W. Bruce , A. A. Du Plessis and C. T. C. Wall . Determinacy and unipotency. Invent. math. 88 (1987), 521554.

[8]E. Kunz . The value semigroup of a one-dimensional Gorenstein ring. Proc. Amer. Math. Soc. 25 (1970), 748751.

[15]C. T. C. Wall . Finite determinacy of smooth map germs. Bull. London Math. Soc. 13 (1981), 481539.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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