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Ternary quartics and 3-dimensional commutative algebras. (English) Zbl 0910.14011

A structure of a commutative algebra on \(\mathbb{C}^3\) is called a 3-dimensional algebra. Let \({\mathcal A}\) be the set of 3-dimensional algebras. Consider \({\mathcal A}\) as a linear space. Let \({\mathcal A}_0 \subset {\mathcal A}\) be the linear subspace of algebras with trivial trace. By definition, \(\eta\in {\mathcal A}_0\) if the contraction of the structure tensor of \(\eta\) is equal to zero.
In this paper we find a connection between 3-dimensional commutative algebras with trivial trace and plane quartics and their bitangents.

MSC:

14H50 Plane and space curves
15A78 Other algebras built from modules
13C99 Theory of modules and ideals in commutative rings
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