For purposes of this question "terminal symplectic variety" means a normal variety which is symplectic (in the usual sense of symplectic singularities) and whose singular locus has codimension $\geq 4$ (the equivalence of this with the usual definition of terminal is a theorem of Namikawa). 


Symplectic varieties has lots of nice properties; For example, they are always Cohen-Macaulay, which is a condition about niceness with respect to depth. So, one can hope for others.



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> Is a terminal symplectic variety necessarily $S\_4$?
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I should warn any potential answerers that my understanding of the $S\_4$ property is very poor (it's an exceptionally tough thing to Google, since it's not even the dominant use of that term in mathematics). I hesitate to even give a definition for fear of messing it up; I believe it means that every ideal sheaf of codimension $\leq 3$ has depth equal to its codimension. 



Is a terminal symplectic variety S_4?
Ben,


a terminal singularity is Cohen-Macaulay and Cohen-Macaulay implies $S\_n$ for all $n$.


By the way, I already mentioned this in my [answer](https://mathoverflow.net/questions/63257/do-some-of-the-local-cohomology-groups-of-the-structure-sheaf-on-the-singular-loc/63261#63261) to your previous question about this issue. ([here](https://mathoverflow.net/questions/63257/do-some-of-the-local-cohomology-groups-of-the-structure-sheaf-on-the-singular-loc/63261#63261)).


