The course webpage is here (http://tinyurl.com/FOAG1112). The course notes are here.
September 19, 2011
Math 216: Foundations of algebraic geometry 2011-12
Posted by ravivakil under 2011-12 course[3] Comments
[3] Comments
September 19, 2011
October 5, 2011 at 2:35 pm
[...] sections. I’ll be posting revisions over the next academic year, in response to comments from the course, comments here (both new and old), and a large number of emails I’m gradually going [...]
October 19, 2011 at 8:47 am
Copied from an email of Aaron Mazel-Gee, so I can deal with these comments as I deal with other comments (I’ll try to put many “things to do” here, as some may not be dealt with in as timely a manner as I would like). I’ve told him that I want more like this, as they are very helpful.
Hello Prof. Vakil,
I’m taking algebraic geometry with Martin Olsson across the bay, and we’ve been using your book as a reference. Whenever I’m reading a book I tend to make corrections to errors as I find them, and so I’ve been compiling a list which you can find below (basically all notational/typographical, no real math issues). We had been reading from the 7/21/2011 version but we recently switched to the 10/5/2011 version, so I figured I’d send these along instead of sitting on potentially outdated corrections until I finally finish reading the whole book!
The book is really, really great, by the way. It’s incredibly readable, which seems to be no small feat for an algebraic geometry text. I really appreciate the annotations on the exercises, too. Nobody is going to do every exercise (or at least, most people won’t), so it really helps to know how they fit into the bigger picture.
Best,
Aaron Mazel-Gee
from July 21, 2011 version:
On page 68 at the top, “denoted” should be “denote”.
On page 69 at the top, “behaves the way one expect” should be “one expects” or “one would expect”.
Presumably this will be fixed in a final version, but the title for section 3.7 is orphaned at the bottom of 78.
Theorem 3.7.1 is missing a period at the end.
The first sentence of Exercise 4.2.O should probably be “If…then…”; it doesn’t make sense as it is.
In 4.6.H.(a), the phrase “by showing that I is prime” is slightly redundant/misleading. We showed in 4.6.B that Spec(A) is irreducible if A is an integral domain, so following the hint takes us all the way to the result.
In the second paragraph of 5.4.9, it should be “… (n+1) open sets, one for each i=0,…,n”.
from October 5, 2011 version:
The sentence between 6.2.B and 6.2.C is a repeat, it was already stated at the top of the page.
In 6.2.D it should say “all points of X”, not “all points of x”.
In Definition 6.4.4, the parentheses should say “…that this notion IS affine local…”.
In Exercise 6.4.K, it should say “if a homogeneous element factors…”.
In third paragraph of Section 6.5, it should say “with different amounts…”.
7.3.J is missing a period at the end.
In 7.3.L, the subscripts in the notation for the stalk are reversed.
[To be continued, if this is helpful...]
October 19, 2011 at 12:39 pm
Thanks! All the changes are made, except for the following. About formatting (the title for section 3.7): as you say, I’ll worry about that at the end (if there ever is one…) as things will move around. It took me a minute to realize what you meant about about 4.6.H(a), but I then realized you were completely right.