The ample cone consists of real numerical divisor classes represented by ample real divisors. It is an open convex cone, and Kleiman's criterion identifies it with the interior of the nef cone.
The sum of a nef real Cartier class and an ample real Cartier class on a projective scheme is ample. By Kleiman's criterion, the ample cone is the interior of the nef cone. If a ball about an ample class lies in that convex cone, translating it by a nef class still lies in the cone. The sum is consequently still an interior point.

Ancestors (10)

  1. Nef cone
  2. Real numerical divisor classes
  3. Numerical equivalence of divisors
  4. Positivity of divisors
  5. Cartier divisor
  6. Algebraic geometry
  7. Geometry and topology
  8. Area of mathematics
  9. Mathematics
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