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Sep 21, 2011 at 9:34 comment added Sasha Yes, I added the argument showing that this is almost always the case.
Sep 21, 2011 at 9:33 history edited Sasha CC BY-SA 3.0
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Sep 21, 2011 at 8:03 comment added Nick [correction: I meant "for all the other known surfaces in $P^4$"]
Sep 21, 2011 at 8:00 comment added Nick Thank you. So if I understand correctly, besides the HM surface, for all the other surfaces in $\mathbb P^4$, which are residual intersection, the canonical class of the subvariety is not a restriction of the ambient variety?
Sep 21, 2011 at 7:00 history answered Sasha CC BY-SA 3.0