MA 206 0 Algebraic Geometry
Spring 2017-2018

Instructor: Dan Abramovich
Class meeting: Mondays, Wednesdays and Fridays at 11:00-11:50am in Kassar 105
Office: Kassar 112 / 118
Telephone: (401) 863 7968
E-mail: abrmovic ( at ) math (period) brown (dot) edu
Web site:
VERY Preliminary Office hours: Monday, Wednesday 10-11 am; Friday 2:00-3:00, or by appointment (I sometime require ofice hour attendance)
Homework page: here
Presentation page: here

Text: Algebraic Geometry and arithmetic curves by Qing Liu, Oxford Graduate Texts in Mathematics, ISBN 978-0199202492.
With a Brown University login you can read the current edition of the book online. Individual chapters of the previous 2002 edition may be downloaded in PDF.
The author's list of errata here.

Supplementary textbooks

Ravi Vakil, The rising sea: Foundations of algebraic geoemtry).

János Kollár, Lectures on resolution of singularities, Princeton University Press, also available through Brown's library web page using your Brown login.

Algebraic Geometry by Robin Hartshorne, Springer-Verlag, Cor. 8th printing, 1997, ISBN: 0-540-90244-9

Sheaves of modules

Introduction to resolution of singularities

A few presentations following Kollar

Crash course on cohomology

I will start with as much of sheaves of modules and differentials as needed for the rest. Then we'll go through resolution of singularities in characteristic 0 following Kollár. Then we'll do divisors and algebraic curves and proceed as time permits.

The subject of resolution of singularities in characteristic 0 was traditionally considered scary. This is an outdated view which no longer is based on reality. One of my goals is that you will come to know that resolution of singularities - in characteristic 0 - is not so hard. When you go out into the world people will think you have superpowers.

Another goal is for you to help me prepare for my ICM talk.

Basis for grading
When we study material in Liu's book I'll assign weekly homework. When we study resolution of singularities, algebraic curves, and other topics if time permits, students will also present material from the sources in class and submit their notes. Grades will be based on these solutions, presentations and notes.

Solutions to problem sets are to be stapled.


You are encouraged to collaborate with other students in the class on your homework, although I suggest that you think carefully about each problem on your own first. You are required to write up your solutions separately and write the names of the students with whom you worked on the assignment. (You may only use the Internet as a general reference, at the level of generality of Wikipedia.)
You are also encouraged to collaborate on preparation of presentations.

How much time will this class take?

Roughly speaking, you should expect to spend twelve hours every week outside of class, including attending office hours, reviewing class material, doing problem sets, preparing presentations. In addition to three hours of class every week, I estimate a total of 15*13 = 195 hours of time spent on this class.

Dates (see also the academic calendar)

Class starts January 24.
Add date is February 6. Grade option date is February 21 and Audit date March 9.
Between February 12 and 16 there will be special lectures and no office hours.
February 19 Brown is out for President's Day.
Spring break March 26-30.
let me know if you want to go to
AGNES April 13. (Registration deadline has passed.)
Watch for possible updates regarding April 16-20.
Last class May 7 (during reading period).

Accommodations for students with disabilities

Please contact me as early in the semester as possible so that we may arrange reasonable accommodations for a disability. As part of this process, please be in touch with Student and Employee Accessibility Services by calling 401-863-9588 or online at