affine space
Definition.
Let be a field and let be a positive integer. In algebraic geometry we define affine space (or affine -space) to be the set
Affine space is usually denoted by or (or if we want to emphasize the field of definition).
In Algebraic Geometry, we consider affine space as a topological space, with the usual Zariski topology (see also algebraic set, affine variety). The polynomials in the ring are regarded as functions (algebraic functions) on . “Gluing” several copies of affine space one obtains a projective space.
Lemma.
If is algebraically closed, affine space is an irreducible algebraic variety.
References
- 1 R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York.
Title | affine space |
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Canonical name | AffineSpace |
Date of creation | 2013-03-22 15:14:21 |
Last modified on | 2013-03-22 15:14:21 |
Owner | alozano (2414) |
Last modified by | alozano (2414) |
Numerical id | 8 |
Author | alozano (2414) |
Entry type | Definition |
Classification | msc 14R10 |
Classification | msc 14-00 |
Related topic | ProjectiveSpace |
Related topic | AffineVariety |