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One way to view a symplectic manifold $(M,\omega)$ is as a real line bundle $\pi_1: M\times \mathbb{R}\to M$ equipped with a flat connection $d: \Omega^{k}(M, M\times\mathbb{R})\to \Omega^{k+1}(M, M\...

I'm reading this paper and at page 67, he states that for any line bundle $L$ over a Rieman surface there is a connection $A$ whose curvature is $$ F(A)=(\deg L)\omega, $$ where $\omega$ is a positive ...

Let $L$ be a line bundle over a compact complex manifold $X$ with a Hermitian metric $\omega$: $L$ is said numerically effective (nef, for short) if for any $\epsilon>0$ there exists a smooth ...