# Minimal size of an open affine cover for an open complement

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 $$X$$?

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