Abstract
The most important invariant of a linear subspace of affine space is its dimension. For affine varieties, we have seen numerous examples which have a clearly defined dimension, at least from a naive point of view. In this chapter, we will carefully define the dimension of any affine or projective variety and show how to compute it. We will also show that this notion accords well with what we would expect intuitively. In keeping with our general philosophy, we consider the computational side of dimension theory right from the outset.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Cox, D., Little, J., O’Shea, D. (2007). The Dimension of a Variety. In: Ideals, Varieties, and Algorithms. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-35651-8_9
Download citation
DOI: https://doi.org/10.1007/978-0-387-35651-8_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-35650-1
Online ISBN: 978-0-387-35651-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)