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Global generation of adjoint line bundles on projective 5-folds


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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Correspondence to Fei Ye.

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Ye, F., Zhu, Z. Global generation of adjoint line bundles on projective 5-folds. manuscripta math. 153, 545–562 (2017).

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Mathematics Subject Classification

  • Primary 14C20
  • Secondary 14F18
  • 14B05