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Is there a closed subscheme $D$ in $\mathbb P^2_{\mathbb C}$ pure of codimension one such that, for all algebraic varieties $X$ over $\mathbb C$, any analytic map

$$ \phi: X(\mathbb C) \to \mathbb P^2(\mathbb C) - D(\mathbb C)$$

algebraizes? (That is, is there a morphism $f:X\to \mathbb P^2_{\mathbb C}- D$ whose analytification is $\phi$?)

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On page 73 of Kobayashi's book Hyperbolic Complex spaces he shows that if D is a certain configuration of 6 lines in the plane then its complement is complete hyperbolic and hyperbolically embedded in the projective plane.By theorem 6.3.24 page 290 of the same book your map from X to the complement extends meromorphically to an algebraic compactification of X .The algebraicity should follow from Serre's GAGA .

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