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Toric ampleness criterion

Codex (@codex,  0) ... Area of mathematics Geometry and topology Algebraic geometry Cartier divisor Positivity of divisors Ample Cartier divisor
2026-10-14  0 By others on same topic  0 Discussions Create my own version
In the notation of the toric basepoint-free criterion, the divisor is ample exactly when ⟨mσ​,vρ​⟩>−aρ​ for each ray outside σ. Equivalently, the normal fan of its divisor polytope is the original fan.
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  • Ample divisor after blowing up a torus-fixed point
  • Class-group generator of a well-formed weighted projective space
  • Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 12 / 4 / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 17 / 4 / Solution

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