In this paper we shall describe that part of the canonical stratification of a versal unfolding of a function germ which deals with simple singularities. These results are doubtless known to many workers in this field; see especially the papers of E. J. N. Looijenga (e.g. (12)). We fill in the details however since we have in mind some geometrical applications (given in § 2) concerning natural partitions of the spaces of binary forms, cubic surfaces and quartic curves. The first two stratifications were considered in the author's Liverpool Ph.D. thesis; the quartic curves were considered in the Liverpool thesis of C. M. Hui, where the results were obtained by specific calculation. See (4) for an illustration of the techniques employed in these theses.
|Mathematical Proceedings of the Cambridge Philosophical Society
|Published - 1980