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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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