Abstract
Let X be a smooth projective variety of dimension 5 and L be an ample line bundle on X such that $$L^5>7^5$$ and $$L^d\cdot Z\ge 7^d$$ for any subvariety Z of dimension $$1\le d\le 4$$ . We show that $$\mathcal {O}_X(K_X+L)$$ is globally generated.
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