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Let $X$ be the algebraic variety over $\mathbb{R}$ obtained from the projective plain $\mathbb{P}^2$ by blowing up one point $P \in \mathbb{P}^2(\mathbb{R})$. Since $X$ is a smooth projective algebraic variety the space of complex points $X(\mathbb{C})$ admits a Kahler structure and hence the underlying $4$-dimensional real manifold admits a symplectic ...

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