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Determinacy of Smooth Germs with Real Isolated Line Singularities
Bohao Sun and Leslie C. Wilson
Proceedings of the American Mathematical Society
Vol. 129, No. 9 (Sep., 2001), pp. 2789-2797
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2668805
Page Count: 9
You can always find the topics here!Topics: Mathematical functions, Analytics, Real lines, Determinacy, Geometric lines, Jacobians, Isolated singularities, Matrices, Mathematical theorems
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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 Łojasiewicz at the singular set, and its Hessian determinant restricted to the singular set is Łojasiewicz at 0. Consider the set of all germs whose singular set contains a fixed nonsingular curve L. We prove that such a germ f is infinitely determined among all such germs with respect to composition by diffeomorphisms preserving L if, and only if, the Jacobian ideal of f contains all germs which vanish on L and are infinitely flat at 0 if, and only if, f is a real isolated line singularity.
Proceedings of the American Mathematical Society © 2001 American Mathematical Society