Commutative algebra 30 Symbolic powers
Channel: Richard E Borcherds
Date: 2020-08-30

This lecture is part of an online course on commutative algebra, following the book
"Commutative algebra with a view toward algebraic geometry" by David Eisenbud.

In this lecture we give some examples related to primary ideals. 
In particular we give an example of a primary ideal that is not a power of a prime ideal, and a power of a prime ideal that is not primary.  We then show that a power of a maximal ideal is primary and use this to define the symbolic powers of a prime ideal. These correspond roughly to functions vanishing to a given order along the zero set of a prime ideal. 

Reading: Section 3.9
Exercises: 3.13