科研之友
微信
新浪微博
Facebook
分享链接
摘要
Let A be an Artinian Gorenstein algebra over an infinite field k of characteristic either 0 or greater than the socle degree of A. To every such algebra and a linear projection pi on its maximal ideal m with range equal to the socle Soc(A) of A, one can associate a certain algebraic hypersurface S-pi subset of m, which is the graph of a polynomial map P-pi : ker pi -> Soc(A) similar or equal to k. Recently, the following surprising criterion has been obtained: two Artinian Gorenstein algebras A, A are isomorphic if and only if any two hypersurfaces S-pi and S-(pi) over bar arising from A and A, respectively, are affinely equivalent. The proof is indirect and relies on a geometric argument. In the present paper, we give a short algebraic proof of this statement. We also discuss a connection, established elsewhere, between the polynomials P-pi and Macaulay inverse systems.
- 出版日期2016
