A semiample divisor on an integral projective variety is ample if it has positive degree on every integral projective curve. Its Kodaira map cannot contract a positive-dimensional fibre, since such a fibre contains a curve and the pulled-back hyperplane bundle has degree zero there. Thus the morphism is proper and a quasi-finite morphism, hence a finite morphism. The finite pullback of an ample line bundle is ample.

Ancestors (8)

  1. Semiample divisor
  2. Positivity of divisors
  3. Cartier divisor
  4. Algebraic geometry
  5. Geometry and topology
  6. Area of mathematics
  7. Mathematics
  8. Home

Incoming links (2)

View article source

Discussion (0)

New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version