Determinacy of smooth germs with real isolated line singularities

Authors:
Bohao Sun and Leslie C. Wilson

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2789-2797

MSC (1991):
Primary 58K40; Secondary 32S05

DOI:
https://doi.org/10.1090/S0002-9939-01-06068-3

Published electronically:
February 9, 2001

MathSciNet review:
1838804

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Abstract | References | Similar Articles | Additional Information

The germ of a smooth real-valued function on Euclidean space is called a real isolated line singularity if its singular set is a nonsingular curve, its Jacobian ideal is ojasiewicz at the singular set, and its Hessian determinant restricted to the singular set is ojasiewicz at 0. Consider the set of all germs whose singular set contains a fixed nonsingular curve . We prove that such a germ is infinitely determined among all such germs with respect to composition by diffeomorphisms preserving if, and only if, the Jacobian ideal of contains all germs which vanish on and are infinitely flat at 0 if, and only if, is a real isolated line singularity.

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Additional Information

**Bohao Sun**

Affiliation:
Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822

**Leslie C. Wilson**

Affiliation:
Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822

Email:
les@math.hawaii.edu

DOI:
https://doi.org/10.1090/S0002-9939-01-06068-3

Keywords:
Non-isolated singularities,
line singularities,
infinite determinacy,
Lojasiewicz inequality

Received by editor(s):
January 5, 2000

Published electronically:
February 9, 2001

Communicated by:
Jozef Dodziuk

Article copyright:
© Copyright 2001
American Mathematical Society