Algebraic geometry Classical varieties Concept
Affine variety
Summary
An affine variety is an irreducible algebraic set in affine space over an algebraically closed field . Affine varieties are the local building blocks of all algebraic varieties. An affine variety corresponds to a prime ideal of the polynomial ring, and it is determined up to isomorphism by its coordinate ring. Some authors drop the irreducibility condition and call every algebraic set an affine variety.
Where this leads
12 pages build on this one.
Further reading
About this page
| Tag | JERVQT4C12 |
|---|---|
| URI | m2://JERVQT4C12 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 14A10 |
| Specializes | Algebraic set |
| Same as |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- a source with a locator (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Used by
- Complete intersection
- Quasi-projective variety
- Dimension of an algebraic variety
- Algebraic variety
- Coordinate ring
- Regular function
- Zariski tangent space
- Projective variety
- Singular point of an algebraic variety
- Function field of a variety
- Morphism of varieties