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Many local rings have geometric interpretations. Cohen–Macaulay rings correspond to equi-dimensionality, and regular local rings correspond to non-singularity, but what is a geometric interpretation of Gorenstein local rings? I am not able to find one, so suggestions are most welcome!

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    Cohen-Macaulay is much stronger than the equidimensionality which is just a topological property.2012-12-21
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    see [here](http://mathoverflow.net/questions/159536/geometric-interpretation-and-differences-of-gorenstein-rings-complete-intersect)2015-01-09

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