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!
The geometric interpretation of Gorenstein local ring
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algebraic-geometry
commutative-algebra
gorenstein
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2see [here](http://mathoverflow.net/questions/159536/geometric-interpretation-and-differences-of-gorenstein-rings-complete-intersect) – 2015-01-09