# Math 245A Topics in algebraic geometry: Complex
algebraic surfaces

**Lectures:**
We'll meet Wednesdays and Fridays 2:10-3:25 in 380-381T.
(The official time is Monday, Wednesday, Friday 2:10-3:05.)
**Office hours:** By appointment, in 380-383M (third floor of the math building).
I will almost always be available to talk at length after each class, and
at other times of the week as well.

**Our goal:**
We develop the theory of (complex) algebraic surfaces, with the goal
of understanding Enriques' classification of surfaces. Some familiarity
with the language of algebraic geometry will be assumed,
although we will develop most of the tools as we need them.
The background assumed will depend on the people attending the class.

** Textbook(s):**

Arnaud Beauville's *Complex algebraic surfaces*.
There are some available at the bookstore; let me know if and
when they run out. I suspect they may not have enough; if that's
the case, there appear to be some new copies for sale at amazon.com.
There are also used (hence cheap) and new copies for sale
at bookfinder.com.
(I've bought lots of cheap used math books at this site.)
Finally, this book is a translation of *Surfaces Algebriques
Complexes* in the Asterisque series. If you can read
French, you may want to buy the original instead.
Miles Reid's *Chapters on Algebraic Surfaces* is available (free!) on the web.
It is available
here; just click on the ``PS'' button, or
choose another format of your choice.
There are a few more references given in the introductory handout.
Miranda's article is available (in ps format) on his webpage
**Notes:**
Notes for many of the classes in dvi, ps, and pdf formats are here.
They are very rough, some rougher than others! I will largely
follow Beauville.
I suspect that the ways I make pdf files are device-dependent (i.e.
they may look funny on your machine), so I've tried three different
ways (pdfA, pdfB, pdfC).
If you try both and one is better than the other, could you please
tell me? I suspect pdfB is better.

The introductory handout
(with incorrect website):
dvi,
ps,
pdfA,
pdfB.
Lecture 1 (Monday, Sept. 30):
dvi,
ps,
pdfA,
pdfB.
Lecture 2 (Wednesday, Oct. 2):
dvi,
ps,
pdfA,
pdfB.
Lecture 3 (Wednesday, Oct. 9):
dvi,
ps,
pdfA,
pdfB.
Lecture 4 (Friday, Oct. 11), notes updated Dec. 19, 2014 to fix an error caught by Konstantin Loginov:
pdf,
Lecture 5 (Wednesday, Oct. 16):
dvi,
ps,
pdfA,
pdfB.
Lecture 6 (Friday, Oct. 18):
dvi,
ps,
pdfA,
pdfB.
Lecture 7 (Wednesday, Oct. 23):
dvi,
ps,
pdfA,
pdfB.
Lecture 8 (Friday, Oct. 25).
dvi,
ps,
pdfA,
pdfB.
Lecture 9 (Wednesday, Oct. 30).
dvi,
ps,
pdfA,
pdfB.
Lecture 10 (Friday, Nov. 1).
dvi,
ps,
pdfA,
pdfB.
Lecture 11 (Wednesday, Nov. 6).
dvi,
ps,
pdfA,
pdfB.
Lecture 12 (Friday, Nov. 8).
dvi,
ps,
pdfA,
pdfB,
pdfC.
Lecture 13 (Wednesday, Nov. 13).
dvi,
ps,
pdfA,
pdfB,
pdfC.
(Aug '08: There is an error on the third page, where
I blow up the plane at 3 points, but insist that no two be on a line;
it should be: no 3 on a line. Thanks to Charles Siegel!)
Lecture 14 (Friday, Nov. 15).
dvi,
ps,
pdfA,
pdfB,
pdfC.
(Thanks to Izzet Coskun for pointing out an error: I erroneously stated that the blow-up of the projective plane at eight points is embedded by the
ver ample linear series -2K (p.2-3); -2K is ample, but not very ample,
and maps the surface 2:1 onto a quadric cone.)
Lecture 15 (Wednesday, Nov. 20).
dvi,
ps,
pdfA,
pdfB,
pdfC.
Lecture 16 (Friday, Nov. 22).
dvi,
ps,
pdfA,
pdfB,
pdfC.
Lecture 17 (Wednesday, Nov. 27).
dvi,
ps,
pdfA,
pdfB,
pdfC
(with a patch on Dec. 6).
No lecture Friday, Nov. 29 (Thanksgiving).
Lecture 18 (Wednesday, Dec. 4).
dvi,
ps,
pdfA,
pdfB,
pdfC.
Lecture 19 (Friday, Dec. 6).
dvi,
ps,
pdfA,
pdfB,
pdfC.

Back to my home page.

Ravi Vakil

Department of Mathematics Rm. 383M

Stanford University

Stanford, CA

Phone: 650-723-7850 (but e-mail is better)

Fax: 650-725-4066

vakil@math.stanford.edu