Math 176: Algebraic Geometry

Fall 2012

Overview

Algebraic geometry is both old and amazingly active. In this course the goal is to become acquainted with the basics, affine and projective varieties, while keeping an eye on modern tools, such as moduli, and fun applications, such as enumerative geometry and number theory.

Instructor

Dagan Karp
1267 Olin
Office hours: Tu/Th 4:00-5:00 p.m., and by appointment

Textbook

We'll use Undergraduate Algebraic Geometry by Miles Reid.
Other good resources include Fulton's Algebraic Curves, An Invitation to Algebraic Geometry by Karen Smith, and the graduate text Algebraic Geometry by Joe Harris.

Grading

Homework 60%
Midterm 15%
Final project 25%

Homework

Written homework will be due Thursdays, and is posted below. Please consult the HMC mathematics homework format guidelines for helpful tips on homework submission and formatting.

Critical Readings

In addition to the written homework, suggested readings will be posted on the homework page in conjunction with upcoming lectures. Before each lecture, read the corresponding material, and bring to class one or two written questions and/or comments.

The goals of the critical reading exercises are manifold: to better the student's independent intake of mathematical exposition, to train in independent learning, to increase the interactive nature of the course (by allowing the instructor to respond to the questions and comments), and to make the course more tailored to the specific curiosities of the class as a whole.

Sakai

There is a Sakai site in conjunction with this class (as with all other Mudd classes). It will be used primarily to share resources, such as notes, and is available only to members of the class.

Tutoring Sessions

In addition to office hours, there will be weekly problem solving/ tutoring sessions. The tutor for this course is Olivia Beckwith. The problem solving sessions will be Tuesdays, 8:00--10:00 p.m., and will be held in the newly renovated third floor of Sprague Library.

LaTeX

Students interested in using LaTeX are encouraged to do so, but it is not required.

Disabilities

Students who need disability-related accommodations are encouraged to discuss this with the instructor as soon as possible.
Homeworks, due Thursdays in class
  • HW 1. Due Thu Sep 6. pdf
    p.s. Be sure to subscribe to math-176-l (using listkeeper@hmc.edu) if you are not already getting e-mails from the list.
  • HW 2. Due Thu Sep 13. pdf
  • HW 3. Due Thu Sep 20
    Reading: Reid Section 1.
    pdf || tex
  • CR 1. Due Tue Sep 25
    Reading: Reid Subsections (2.1) through (2.10)
  • HW 4. Due Thu Sep 27
    Problems: Reid 1.5, 1.6, 1.8, 1.10.
  • CR 2. Due Tue Oct 2
    Reading: Reid Subsections (2.11) through (2.14)
  • HW 5. Due Thu Oct 4
    Problems: Reid 2.1, 2.2, 2.3, 2.4.
  • CR 3. Due Tue Oct 9
    Reading: Reid, Appendix to Chapter I, and Subsections (3.1) through (3.7)
  • HW 6. Due Thu Oct 11
    Problems: Reid 2.5, 2.7, 2.8, 2.9.
  • CR 4. Due Thu Oct 25
    Reading: Reid, Chapter II Section 4
  • HW 7. Due Thu Oct 25
    pdf || tex
  • CR 5. Due Tue Oct 30
    Reading: Re-read Reid, (4.9)-(4.14)
  • HW 8. Due Thu Nov 1
    Reid: 4.2, 4.4, 4.5, 4.7.
  • Midterm Exam Due Thu Nov 8
  • CR 6. Due Tue Nov 13
    Reading: Read Reid, Section 5
  • HW 9. Due Thu Nov 15
    Reid: 4.9, 4.10, 4.11, 4.12.
    Final Project Topic Due
  • CR 7. Due Tue Nov 27
    Reading: Read Reid, Section 6
  • HW 10. Due Thu Nov 29
    Reid: 5.1, 5.2.
  • Final Project Due Tue Dec 4
    Two to Five page LaTeX document due Tue Dec 4.
    20 minute oral presentations begin Tue Dec 4