MATH 681
Algebraic Geometry, Fall 2021

Lectures:

MWF 2, 210 Deady

Office hours:

Monday 3-4, Tuesday 1-2, or by appointment

My office:

207 Deady, phone 3465635, e-mail apolish@uoregon.edu

Textbooks:

We will use the following:

  • "Introduction to commutative algebra" by Atiyah and Macdonald
  • "Algebraic geometry" by Hartshorne

    • Pre-requisites:

    Math 647-649

    Tentative plan:

    Atiyah and Macdonald, chapters 10 and 11; Hartshorne, chapter 1

    Homework

    There will be no exams in this course, so the grade will be based solely on your homework scores. Homework should be turned in by email, as pdf file, on the day when it's due. You are encouraged to collaborate on homeworks, however, writing up the solutions should be an individual work.

    Fall homework assignments:

    Abbreviations: "AM" is Atiyah-Macdonald, "H" is Hartshorne
    The problems marked as "WU" have to be written up and submitted for grading

    Assignment #1 (due October 6):

  • Exercises from AM: 10.1(WU), 10.2, 10.4(WU), 10.6(WU), 10.7, 10.9(WU), 10.10(WU).

    • Assignment #2 (due October 15):

  • Exercises from AM: 11.1(WU), 11.2 (WU), 11.4, 11.6(WU), 11.7(WU).

    • Assignment #3 (due October 22):

  • Exercises from H: 1.1, 1.2 (WU), 1.6, 1.7, 1.8, 1.10, 1.11* (WU); 2.1 (WU), 2.2 (WU), 2.3, 2.4, 2.5, 2.6, 2.7, 2.9(a) (WU), 2.10, 2.11.

    • Assignment #4 (due November 1):

  • Exercises from H: 2.13 (WU), 3.1, 3.3 (WU), 3.5 (WU), 3.10, 3.11, 3.12, 3.14, 3.17 (WU), 3.19(a), 3.21, 4.1 (WU).

    • Assignment #5 (due November 10):

  • Exercises from H: 4.2, 4.3, 4.4, 4.6 (WU), 4.9 (WU), 5.1, 5.3 (WU), 5.4 (WU, (a) is a bit hard, you can skip it at first), 5.8 (WU), 5.9, 5.10, 5.12.

    • Assignment #6 (due November 22):

  • Exercises from AM: 5.12 (WU), 5.13 (WU), 5.14, 5.28, 5.29 (WU), Exercises from H: 5.15, 6.1ab, 6.2abcd (WU), 6.2e, 6.4.