MA 206 0 Algebraic Geometry
Spring 2018-2019

Instructor: Dan Abramovich
Regular class meeting: Mondays, Wednesdays and Fridays at 11:00-11:50am in Kassar 205
Office: Kassar 112 / 118
Telephone: (401) 863 3319
E-mail: abrmovic ( at ) math (period) brown (dot) edu
Web site:
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

Text: This time I did a book at the bookstore, but still the texts, my notes and homework are based on are available through Brown's library web page.
Make sure you can access these since reading - including independent reading - and homework problems will be assigned.

The text ordered:
Algebraic Geometry by Robin Hartshorne, Springer-Verlag, Cor. 8th printing, 1997, ISBN: 0-540-90244-9
Library link here.

Other books:
The geometry of Schemes, by David Eisenbud and Joe Harris, Springer, Graduate texts in mathematics, ISBN: 0387986375 (softcover : alk. paper), 0387986383 (hardcover : alk. paper)
Library link here.

Algebraic Geometry and arithmetic curves by Qing Liu, Oxford Graduate Texts in Mathematics, ISBN 978-0199202492.
Library link here.
The author's list of errata here.

Not yet published:
The rising sea: Foundations of algebraic geoemtry by Ravi Vakil.

Notes in preliminary form:
Quick review

Presentation notes:
Enough injectives (following ogus)

Notes from a previous course (Some might be valuable for review):
Sheaves of modules
Introduction to resolution of singularities
A few presentations following Kollar
Crash course on cohomology

Cohomology of schemes, algebraic curves and algebraic surfaces.

Basis for grading
I'll assign homework from the books, but I am not sure I will grade it. I will assign reading material. I will regularly assign material to present in class, which will be the primary grading mechanism. In fact the entire subject of curves and surfaces will be covered this way.

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 Wednesday January 23.
February 18-19 Brown long weekend.
February 22-March 1 I'll be away. Guest lectures: Melody Chan, February 25; Brendan Hassett, February 27; Joseph Silverman, March 1.
March 23-31 is Brown's Spring Break.
Reading period starts April 26.
Our last possible class will be on May 3.
Academic decision dates: Add date is February 5. Grade option/change date is February 20 and Audit date March 8.

March 22 you may want to attend

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