MATH 682
Algebraic Geometry, Winter 2020

Lectures:

MWF 10, 473 McKenzie

Office hours:

Monday 11-12, or by appointment

My office:

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

Textbooks:

We will use the following:

  • "Algebraic geometry" by Hartshorne
  • Vakil's book

    Pre-requisites:

    Math 647-649

    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 on the day when it's due either in class or at my office (you can slip it under the door). Homework must be stapled. You are encouraged to collaborate on homeworks, however, writing up the solutions should be an individual work.

    Homework assignments:

    Abbreviations: "H" is Hartshorne, "V" is Vakil
    The problems marked as "WU" have to be written up and submitted for grading

    Assignment #1 (due January 17): All exercises from V

  • Ex. 2.2.B, D(b), F, G, I, J
  • Ex. 2.3.A, B, C (WU), D, J (WU)
  • Ex. 2.4.B, D, F (WU), M (WU)
  • Ex. 2.6.A, B (WU)

    • Assignment #2 (due January 29):

  • Ex. H:II.1.14, 1.16 (WU).
  • Ex. V:2.6.G, H, J(b);
  • Ex. V:3.4.H, I; 3.5.E (WU); 3.6.H;
  • Ex. V:4.3.B, D, G (WU); 4.4.A, B, D; 4.5.J,O;
  • (WU) Prove that if I is a homogeneous ideal in a nonnegatively graded ring S then V(I)=V(I_{>n}), where I_{>n} is the ideal of elements of degree >n in I.

    • Assignment #3 (due February 7):

  • Ex. V:5.1.A, B, 5.2.C, D (WU), G, H, I, 5.3.C (WU)
  • Ex. H,ch.II: 2.7 (WU), 2.8 (WU), 2.9 (WU), 2.10, 2.11, 2.16

    • Assignment #4 (due February 17):

  • Ex. V:5.1.G, 7.3.A, 7.3.Ca, 7.3.F (WU), 7.3.I, 7.3.Qc (WU)
  • Ex. H,ch.II: 3.2, 3.8, 3.14, 3.6 (WU), 3.7 (WU), 3.18bc (WU)

    • Assignment #5 (due February 26):

  • Ex. V: 8.1.D (WU), 8.1.Jbd (WU)
  • Ex. H. 3.11a (WU), 3.12 (WU), 3.13

    • Assignment #6 (never due):

  • Ex. V: 10.1.B, 10.1.M, 13.5.A
  • Ex. H: 4.3, 4.9, 4.5(a,b)(c)*, 5.1, 5.4.

    • Return