A stratification of the space of cubic surfaces

Bruce, Bill (1980) A stratification of the space of cubic surfaces. Mathematical Proceedings of the Cambridge Philosophical Society, 87 (3). pp. 427-441. ISSN 0305-0041 DOI https://doi.org/10.1017/S0305004100056863

Item not available from this archive.

Abstract

In (4) the classification of (complex, projective) cubic surfaces by the number and nature of their singularities is carried out. This gives a natural partition of the vector space of cubic surfaces (which we denote by H3(4, 1)). In this paper we investigate the differential geometric properties of this partition; we show that it provides a finite constructible stratification of H3(4,1) which, in the notation of (10), is Whitney (A) regular. In fact Whitney (B) regularity holds over each stratum other than E6, but this stratum of cubic cones has an exceptional (equianharmonic) orbit at which (B) regularity fails. It remains to be seen whether or not this is the only exceptional orbit.

Item Type: Article
Subjects: Q Science > QA Mathematics
Date Deposited: 05 Jan 2011 15:28
URI: http://repository.edgehill.ac.uk/id/eprint/2132

Archive staff only

Item control page Item control page