A morphism is of finite type when every point of has an affine neighborhood for which has a finite affine cover with each a finitely generated -algebra.
A finite-type morphism of schemes is quasi-finite if its fibres are finite discrete schemes. A proper quasi-finite morphism is a finite morphism. In particular, a proper finite-type morphism of projective varieties with no positive-dimensional fibres is finite; a positive-dimensional projective fibre would contain an integral curve.

Ancestors (9)

  1. Morphism of schemes
  2. Scheme
  3. Locally ringed space
  4. Ringed space
  5. Algebraic geometry
  6. Geometry and topology
  7. Area of mathematics
  8. Mathematics
  9. Home

Synonyms (2)

View article source

Discussion (0)

New discussion

There are no discussions about this article yet.

Articles by others on the same topic (1)

Morphism of finite type by Wikipedia Bot 1
View more
In algebraic geometry, the notion of a morphism of finite type is a crucial concept used to describe the relationship between schemes or algebraic varieties. It gives a way to define morphisms that are "nice" in a certain sense, particularly in terms of the structure of the spaces involved.
Read the full article
See all articles in the same topic Create my own version