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2 Some Covariants Related to Steiner Surfaces 45
Conclusion

In this paper, we have produced a collection of covariants for quadratic parameteri-
zations of surfaces. We were guided by the geometry of the Steiner surface. In future
work, we wish to tackle the problem in a more systematic way: exploiting methods
from Invariant Theory, we will try to produce systems of generators for the covari-
ants; or at least to describe all the covariants of low degree.

Acknowledgments
The authors want to thank the readers and anonymous referees, of this paper and of
a previous version, for their constructive remarks.
Emmanuel Briand was supported by the European Research Training Network
RAAG (Real Algebraic and Analytic Geometry), contract No. HPRN-CT-2001-
00271. He wishes to thank the Universidad de Cantabria for its hospitality in 2005.

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