Abstract algebraic variety
From Wikipedia, the free encyclopedia
 |
All or part of this article may be confusing or unclear. Please help clarify the article. Suggestions may be on the talk page. (June 2008) |
 |
This article or section is in need of attention from an expert on the subject. Please help recruit one or improve this article yourself. See the talk page for details. Please consider using {{Expert-subject}} to associate this request with a WikiProject |
 |
To comply with Wikipedia's lead section guidelines, the introduction of this article may need to be rewritten. Please discuss this issue on the talk page and read the layout guide to make sure the section will be inclusive of all essential details. |
In algebraic geometry, an abstract algebraic variety is an algebraic variety defined intrinsically: that is, without reference to an external geometric context. Hartshorne (1976) defines an abstract variety to be an integral, separated scheme of finite type over an algebraically closed field k. One further defines an abstract projective variety to be an abstract variety which is a projective scheme over k, and an abstract quasiprojective variety to be an open subscheme of an abstract projective variety. Then, identifying classical algebraic varieties as schemes, in fact they are identified precisely with the abstract quasiprojective varieties.
[edit] References
Hartshorne, Robin (1976), Algebraic Geometry, New York: Springer-Verlag, pp. 104–105
 |
This geometry-related article is a stub. You can help Wikipedia by expanding it. |
