Math 176: Algebraic Geometry

Fall 2018

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
Office: Shan 3414
Office hours: Tuesday 3:00-4:00 p.m., and open door

Lectures

This course will meet Monday and Wednesday, 1:15-2:30pm in Shanahan room 3421.

Inquiry Based Learning

This course will be centered on an IBL approach to algebraic geometry. Students, rather than the professor, will do most of the talking in class. Much of classtime will be reserved for student presentations of solutions to problems.

Textbook

We'll use Algebraic Geometry: A Problem Solving Approach by Garrity et al.
Other good resources include Fulton's Algebraic Curves, An Invitation to Algebraic Geometry by Karen Smith, and the graduate texts (two distinct texts with the same title) Algebraic Geometry by Joe Harris and Robin Hartshorne.

Course Binder

Each student will maintain a binder, into which hardcopy solutions to problems will be archived. A central goal of the course is to create your own algebraic geometry textbook, in some sense, through your solutions to the problems in the text. The first page of the binder should consist of a three column list, where you record each problem that you work on, weather it was solved or attempted, and whether or not you received help in the form of collaboration.

Exam

There will be one midterm. It will be in-class on Wednesday, October 17.

Grading

Binder 35%
Class Participation 35%
Midterm 20%
Final project 10%

Homework

Written homework will be due on Mondays, with the goal of presenting solutions in class, and keeping a hardcopy LaTeX in your binder. Here are some useful tips for LaTeX homework formatting.

LaTeX

Students must use LaTeX for binder problems.

Disabilities

It is the policy of The Claremont Colleges to accommodate students with temporary or permanent disabilities. Any student with a documented disability who requires reasonable accommodations should contact Deborah Kahn, Coordinator for Student Disability Resources at (909) 607-3148 or dkahn@hmc.edu, as soon as possible. Students from the other Claremont Colleges should contact their home college's disability officer.

Old Course Notes


Homework
    HW 1. Due Mon Sep 10.
    Read Sections 4.1 and 4.2.
    Problems 4.1.3, 4.1.5, 4.1.6, 4.1.8, 4.2.1, 4.2.2, 4.2.5
    HW 2. Due Mon Sep 17.
    Read Sections 4.2 and 4.3.
    Problems 4.2.14 (2), 4.2.15, 4.2.18, 4.2.19, 4.2.20, 4.3.3, 4.3.4
    HW 3. Due Mon Sep 24.
    Read Sections 4.4 and 4.5.
    Problems 4.4.3, 4.4.4, 4.4.5, 4.4.6, 4.5.1, 4.5.15, 4.5.16, 4.5.17
    HW 4. Due Mon Oct 1.
    Read Sections 4.6 and 4.7.
    Problems 4.7.2, 4.7.3, 4.7.6, 4.7.7, 4.7.9, 4.7.10, 4.7.13, 4.7.14.
    Due Mon Oct 8.
    Binder Check: Bring your binders to class on Monday.
    Wed Oct 10.
    No Class
    HW 5. Due Mon Oct 15.
    Read Sections 4.8 and 4.9.
    Problems 4.8.1, 4.8.3, 4.8.4, 4.9.3, 4.9.4, 4.9.8, 4.9.9.
Wed Oct 17: Midterm
Mon Oct 22: No HW (Fall Break)
    HW 6. Due Mon Oct 29.
    Read Sections 4.10 and 4.11.
    Problems 4.11.2, 4.11.3, 4.11.7, 4.11.10, 4.11.11, 4.11.12, 4.11.14.
    HW 7. Due Mon Nov 5.
    Read Sections 18.1 (not 18.2) and 19.
    Problems 18.5, 19.1, 19.2, 19.3, 19.4, 19.5, 19.6, 19.7, 19.8, 19.10.
    HW 8. Due Mon Nov 12.
    Read Sections 1.1-1.5.
    Problems 1.1.18, 1.2.13, 1.2.22, 1.3.7, 1.4.7, 1.4.9, 1.4.19, 1.5.2.
    HW 9. Due Mon Nov 19
    Read Sections 1.6, 1.9, 1.10, 1.11, 1.12
    Problems 1.9.4, 1.9.8, 1.10.2, 1.10.4, 1.10.5, 1.11.2, 1.12.3.
    HW 10. Due Mon Dec 3
    Read Sections 2.1-2.3, 3.1-3.3, 3.5, 3.6
    Problems 2.2.11, 2.3.5, 2.3.7, 3.3.30, 3.5.11, 3.5.17, 3.5.33, 3.6.35, 3.6.54.
    Final Project

    Due Mon Dec 10: Oral Presentation. Give a 5 minute oral presentation on your chosen topic in, or application of, algebraic geometry which hasn't been covered in the course. Your talk should use roughly 5 slides. Submit your slides to your dropbox in Sakai by 10am on Monday, December 10.

    Due Wed Dec 12: Written exposition. Write a 2-5 page paper describing a topic in algebraic geometry. Your piece should be written as though it could be included seamlessly in a future edition of a text book, and you must use at least one outside source (aside from wikipedia). Your paper must be typset in latex.

    Binder Submission Dec 19

    Complete binders due Wednesday, December 19 by 5pm to Prof Karp's office.