A stratification of the space of cubic surfaces

Bill Bruce

    Research output: Contribution to journalArticle

    11 Citations (Scopus)

    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.
    Original languageEnglish
    Pages (from-to)427-441
    JournalMathematical Proceedings of the Cambridge Philosophical Society
    Volume87
    Issue number3
    DOIs
    Publication statusPublished - 1980

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