Let $X$ be a smooth projective scheme and $Y$ be a projective subscheme of $X$, not necessarily smooth. Are there any known results about the minimal size of an open affine cover (number of affines in the cover) for the complement of $Y$ in $X$?

  • $\begingroup$ Can you tell us what you mean by `size'? Number of open sets? $\endgroup$ – Mohan Feb 11 at 14:15
  • $\begingroup$ Yes, that's what i mean. $\endgroup$ – Christoph Feb 11 at 14:47
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    $\begingroup$ If $\dim X=n$, ($X$ a smooth projective variety over a field) then typically you would need $n+1$ in general. $\endgroup$ – Mohan Feb 11 at 16:25

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