My question is about this and this:
In the first link Graham Leuschke says: "That is a hypersurface ring, so Gorenstein, so the canonical module is the ring itself."
What is a hypersurface ring and why is it Gorenstein?
Thanks.
2026-02-22 20:59:20.1771793960
What is a hypersurface ring and why is it Gorenstein?
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Searching "hypersurface ring" at googlebooks immediately got me this (pg 28):
Graham Leuschke was just introducing this terminology for that particular combination of conditions.
The answer to "why is it Gorenstein" is precisely the question asked at the second question you linked.Update: Despite the similarity of the definition and the title of the other question, user26857 assured me that the above definition is not sufficient to be Gorenstein. After a bit of searching, I've concluded that Graham Leuschke is either using a different definition, or else had a momentary lapse during that statement. It would be wonderful if he could make some comment on the issue himself!