Gorenstein scheme
Not to be confused with Gorenstein ring.
In algebraic geometry, a Gorenstein variety is a normal algebraic variety whose canonical divisor is Cartier.[1] A Gorenstein scheme can be defined as a generalization of this. If "Cartier" is replaced by ℚ-Cartier, then one obtains the notation of a ℚ-Gorenstein scheme.
A local ring of a Gorenstein scheme need not be Cohen–Macaulay; in particular, need not be Gorenstein.
Some authors (such as the stacks project) require a Gorenstein scheme to be Cohen–Macaulay (i.e., the local rings are Cohen–Macaulay ring.)
Notes
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