Primary References

The primary references for the class are:

We won’t follow either book linearly: we’ll jump around within and between these two books.

[CLO15] is available freely to everyone in the UCSD community thanks to an institutional subscription to Springer Link. If you are off-campus, you may have to use VPN for access. [Ful08] went out of print and is now made available freely to everyone on the internet by the author.

Other References

There are so many! Here’s a list. Feel free to ask for help if you’re looking for something in particular.

Here are some that are roughly at the same level as our course, though each has its own style and emphasis.

A special kind of curve, called an elliptic curve, plays a particularly important role in mathematics, especially number theory and cryptography. Here are some books about elliptic curves.

A class of varieties called toric varieties provides a fertile testing ground for ideas in algebraic geometry, and they are also very useful for a number of applications of algebraic geometry (eg, to statistics). Here are some books about toric varieties.

Here are some that discuss more about computational aspects of algebraic geometry. There’s some intersection here with some of the books listed above about toric varieties.

Modern algebraic geometry uses the language of schemes. Here are some references about this. Some of these books start with introductory chapters about “classical” algebraic geometry.