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Nilpotent algebras and affinely homogeneous surfaces. (English) Zbl 1254.14053
To a nilpotent commutative algebra $$N$$ of finite dimension over a field of zero characteristic one associates a smooth algebraic subvariety $$S \subset N$$, whose degree is the nil-index and whose codimension is the dimension of the annihilator $$A$$ of $$N$$. The case when $$N$$ is graded and $$A$$ is 1-dimensional is studied in detail, in particular the question to what extent the hypersurface $$S$$ determines the algebra $$N$$. A key example with nil-index 5 is given.

##### MSC:
 14J70 Hypersurfaces and algebraic geometry 32V40 Real submanifolds in complex manifolds
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##### References:
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