Nilpotent algebras and affinely homogeneous surfaces. (English) Zbl 1254.14053

Fels, Gregor; Kaup, Wilhelm

Math. Ann. 353, No. 4, 1315-1350 (2012).

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.

Reviewer: Alexandru Dimca (Nice)

MSC:

14J70	Hypersurfaces and algebraic geometry
32V40	Real submanifolds in complex manifolds

Keywords:

nilpotent commutative algebra; smooth subvariety; annihilator

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