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Compositio Mathematica Compositio Mathematica

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Generic Projections in the Semi-nice Dimensions

Published online by Cambridge University Press:  04 December 2007

A. A. Du Plessis  and
C. T. C. Wall
A. A. Du Plessis
Affiliation:
Matematisk Institut, Aarhus Universitet, Ny Munkegade, DK-8000 AarhusC, Denmark
C. T. C. Wall
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, United Kingdom
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Abstract

In his celebrated paper ‘Generic Projections’, Mather obtained the key result that a generic projection to an affine subspace of a smooth submanifold in Euclidean space is jet-transverse to any ‘modular’ submanifold of (multi-) jet space. He also gave an explicit stratification by modular submanifolds, and used it to conclude that the projection, if in the nice dimensions, is generically (C∞-) stable. In this article, we extend the result to the semi-nice dimensions (where only C0-stability is obtained), using the stratification given in our book. We first recall the definitions of the nice and semi-nice dimensions, review the main known results which involve them, and proceed to the statement of our main results. Next we discuss the condition of modularity, and present a number of methods for establishing modularity of particular strata. Finally, we show that all the strata needed for the main result are covered by these methods.

Keywords

canonical stratification generic projections modular submanifold nice dimensions
Type
Research Article
Information
Compositio Mathematica , Volume 135 , Issue 2 , January 2003 , pp. 179 - 209
Copyright
© 2003 Kluwer Academic Publishers

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