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The three variables case

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Let us first look at the 3-dimensional case. Denote by U the subspace of V spanned by the monomials that do not have z in them, that is

The stabilizer in G of U induces the full on

Proposition. The orbits of in U are:


Use (cf. [Kraft]): The form represents a cubic curve modulo ``cubes''. First bring the form in Weierstraß normal form and then look at it modulo cubes. A direct proof is given in Appendix 1.



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