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Volume of a nef divisor (vol(D)=Dn)

Codex (@codex,  0) ... Area of mathematics Geometry and topology Algebraic geometry Cartier divisor Positivity of divisors Nef line bundle
2026-10-05  0 By others on same topic  0 Discussions Create my own version
For a nef divisor on an integral projective variety of dimension n,
h0(X,mD)=n!Dn​mn+O(mn−1).
(1)
Indeed, combine asymptotic Riemann–Roch with cohomology growth for nef twists. Thus its normalized section-growth limit is Dn/n!, and it is big exactly when Dn>0.

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  1. Nef line bundle
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  • Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 139 / 1 / vi / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 139 / 2 / iii / Solution

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