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aglearner
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aglearner
aglearner
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Let $X$ be a smooth compact complex manifold of dimension $n$. Suppose $L$ is a line bundle on $X$ such that $dim(H^0(X,L^k))>c\cdot n^k$$dim(H^0(X,L^k))>c\cdot k^n$ for $c>0$ and $k>>0$.

Question. Is it true that $X$ is Moishezon? Is there some reference for this statement?

Let $X$ be a smooth compact complex manifold of dimension $n$. Suppose $L$ is a line bundle on $X$ such that $dim(H^0(X,L^k))>c\cdot n^k$ for $c>0$ and $k>>0$.

Question. Is it true that $X$ is Moishezon? Is there some reference for this statement?

Let $X$ be a smooth compact complex manifold of dimension $n$. Suppose $L$ is a line bundle on $X$ such that $dim(H^0(X,L^k))>c\cdot k^n$ for $c>0$ and $k>>0$.

Question. Is it true that $X$ is Moishezon? Is there some reference for this statement?

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aglearner
aglearner
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A characterization of Moishezon manifolds via sections of $L^k$ with $k\to \infty$

Let $X$ be a smooth compact complex manifold of dimension $n$. Suppose $L$ is a line bundle on $X$ such that $dim(H^0(X,L^k))>c\cdot n^k$ for $c>0$ and $k>>0$.

Question. Is it true that $X$ is Moishezon? Is there some reference for this statement?