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A stratification of the space of cubic surfaces

Published online by Cambridge University Press:  24 October 2008

J. W. Bruce
J. W. Bruce
Affiliation:
University of Liverpool
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 3 , May 1980 , pp. 427 - 441
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

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