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Homotopy theory, homological algebra, algebraic treatments of manifolds.

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Homeomorphism between del Pezzo surfaces

Let $X$ and $Y$ be smooth del Pezzo surfaces of the same degree $K_X^2=K_Y^2$. Are the sets $X(\mathbb{C})$ and $Y(\mathbb{C})$ homeomorphic, or at least homotopy equivalent?
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