Abstract
This chapter is concerned mainly with the dimension-theoretical analysis of morphisms between varieties. This involves substantially more commutative algebra than has been used up to now. Thus, Section 1 establishes Noether’s Normalization Theorem, which is used for reducing some of the required ideal theoretical considerations to the situation of an ordinary polynomial algebra. The remaining results of Section 1 concern the connections between the dimensions of irreducible closed subvarieties of irreducible affine varieties and the generation of their annihilating ideals.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Hochschild, G.P. (1981). Morphisms of Varieties and Dimension. In: Basic Theory of Algebraic Groups and Lie Algebras. Graduate Texts in Mathematics, vol 75. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8114-3_10
Download citation
DOI: https://doi.org/10.1007/978-1-4613-8114-3_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-8116-7
Online ISBN: 978-1-4613-8114-3
eBook Packages: Springer Book Archive