Abstract
The paper studies generic commutative and anticommutative algebras of a fixed dimension, their invariants, covariants and algebraic properties (e.g., the structure of subalgebras). In the case of 4-dimensional anticommutative algebras a construction is given that links the associated cubic surface and the 27 lines on it with the structure of subalgebras of the algebra. The rationality of the corresponding moduli variety is proved. In the case of 3-dimensional commutative algebras a new proof of a recent theorem of Katsylo and Mikhailov about the 28 bitangents to the associated plane quartic is given.
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The research was supported by Grant # MQZ300 from the ISF and Russian Government.
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Tevelev, E.A. Generic algebras. Transformation Groups 1, 127–151 (1996). https://doi.org/10.1007/BF02587739
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DOI: https://doi.org/10.1007/BF02587739