## Big line bundle [closed]

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On a Moishezon manifold,is a big line bundle nef?Why?

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Terminology? Motivation? Anything? – David Hansen May 24 2011 at 1:25

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Why would it be? Being big is very much a birational notion. Being nef is very much not. – Sándor Kovács May 24 2011 at 1:35

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p.s.: By the way, let $B$ be an arbitrary big line bundle and $E$ an arbitrary line bundle that has a global section, but which is not nef (i.e., there exists a (compact) curve $C$ such that $E|_C$ has negative degree). Then $B\otimes E^{\otimes m}$ is big for any $m\geq 0$, but not nef for $m\gg 0$. This works on any manifold/variety/scheme/space when the notions big and nef make sense. – Sándor Kovács May 24 2011 at 4:21
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