On a new criterion for isomorphism of Gorenstein algebras

Details On a new criterion for isomorphism of Gorenstein algebras On a new criterion for isomorphism of Gorenstein algebras

2012-01-30

arxiv.org/abs/1201.6100v1

Mathematics

Commutative Algebra

Scientific paper

To every Gorenstein algebra $A$ of finite vector space dimension greater than 1 over a field of characteristic zero, and a linear projection $\pi$ on its maximal ideal ${\mathfrak m}$ with range equal to the annihilator of ${\mathfrak m}$, one can associate a certain algebraic hypersurface $S_{\pi}\subset{\mathfrak m}$. Recently, the following surprising criterion has been obtained: two Gorenstein algebras $A$, $\tilde A$ are isomorphic if and only if any two hypersurfaces $S_{\pi}$ and $S_{\tilde\pi}$ arising from $A$ and $\tilde A$, respectively, are affinely equivalent. The proof is indirect and relies on a CR-geometric argument. In the present paper we give a short algebraic proof of this statement.

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