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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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Is it always true that the complement of an ample divisor is affine?

Consider a proper and integral scheme $X\rightarrow\operatorname{Spec}(A)$ over a Noetherian ring $A$ and $D\in\operatorname{Div}(X)$ an effective ample Cartier divisor on $X$. Is it true that its com …
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