Fall 2018-2019

**Instructor:** Dan Abramovich

**Regular class meeting:** Mondays, Wednesdays and Fridays at 11:00-11:50am in Kassar 105

**Office:** Kassar 112 / 118

**Telephone:** (401) 863 3319

**E-mail:** `abrmovic ( at ) math (period) brown (dot) edu`

**Web site:**
`http://www.math.brown.edu/~abrmovic/MA/f1819/index.html`

**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:** I did not order a book at the bookstore, but 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.

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

Library link here.

**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 from a previous course (with varying degrees of relevance) **

Sheaves of modules

Introduction to resolution of singularities

A few presentations following Kollar

Crash course on cohomology

**Subjects**

Very brief discussion of varieties, and then we'll study schemes and some cohomology of schemes.

**Basis for grading**

I'll assign homework from the books and grade it. I will assign reading material. I may assign material to present in class.
If there is an exam it will be a take-home exam.

Your solutions to problem sets are to be stapled.

**Collaboration**

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 September 5.

Monday September 8 I am out for Rosh Hashana and Wednesday September 19 for Yom Kippur.

Monday October 8 Brown is out for Indigenous Peoples Day.

Wednesday October 10 and Friday October 12 I remain out for a conference.

Wednesday October 24 I am scheduled for jury duty and will likely be out (I am supposed to check the night before).

Friday November 23 Brown is out for Thanksgiving weekend.

**Academic decision dates:** Add date is September 20. Grade option/change date is
October 2 and Audit date October 19.

You may want to attend
AGNES
September 21-23. (Registration deadline has passed, but let Lori at the office know.)

Last class December 12 (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

http://brown.edu/Student_Services/Office_of_Student_Life/seas/index.html