Math 145: Undergraduate Algebraic Geometry

 Spring 2024

MWF 09:30 AM - 10:20 AM, GESB150.
This is a undergraduate course in classical algebraic geometry. Geometric intuition will be emphasized. In the first half you will learn the language and dictionary of algebraic geometry, including affine varieties and maps between them, Hilbert basis theorem and Nullstellensatz. In the second half, you will learn more about algebraic curves. A key topic is Bézout's theorem and basic intersection theory. You may also learn about resolution of singularity and the Riemann-Roch theorem. Moreover, we will find many enjoyable applications of alegbraic geometry. We will try to learn about how to invent and develop algebraic geometry by yourself.

Instructor: Zhiyu Zhang (zyuzhang@stanford.edu).

Course assistant: Jiahao Niu (jhniu@stanford.edu).

Office Hour: (Zhiyu) Tuesday 12:30-2:30 pm, Room 382-C. (Jiahao) Thursday 10:30 am-12:30 pm, 3-4:30 pm, Room 381-B.

Prerequisites: Math 120: Groups and Rings.

Textbook: Algebraic Curves (Fulton). Available at Fulton's webpage .

Additional material (optional): Plane Algebraic Curves by Andreas Gathmann. Algebraic Geometry I by Peter Scholze. See also previous Math 145 course (Brain Conrad) and Math 145 course (Ravi Vakil).

Syllabus: Here .

Final grade: 70% Homework, 30% take-home writtings.

Homework (Due Tuesday 11:59 pm each week):

  • Problem Set 1
  • Problem Set 2
  • Problem Set 3
  • Problem Set 4
  • Problem Set 5
  • Problem Set 6
  • Problem Set 7
  • Problem Set 8

    Lecture Schedule:
  • Lecture 1, April 1.
  • Lecture 2, April 3.
  • Lecture 3, April 5.
  • Lecture 4, April 8.
  • Lecture 5, April 10.
  • Lecture 6, April 12.
  • Lecture 7, April 15.
  • Lecture 8, April 17.
  • Lecture 9, April 19.
  • Lecture 10, April 22.
  • Lecture 11, April 24.
  • Lecture 12, April 26.
  • Lecture 13, April 29.
  • Lecture 14, May 1.
  • Lecture 15, May 3.
  • Lecture 16, May 6.
  • Lecture 17, May 8.
  • Lecture 18, May 10.
  • Lecture 19, May 13.
  • Lecture 20, May 15.
  • Lecture 21, May 17.
  • Lecture 22, May 20.
  • Lecture 23, May 22.
  • Lecture 24, May 24.
  • May 27 (Memorial Day).
  • Lecture 25, May 29.
  • Lecture 26, May 31.
  • Lecture 27, June 3.
  • Lecture 28, June 5.

    Access and Accommodations
    Stanford is committed to providing equal educational opportunities for disabled students. Disabled students are a valued and essential part of the Stanford community. We welcome you to our class.
    If you experience disability, please register with the Office of Accessible Education (OAE). Professional staff will evaluate your needs, support appropriate and reasonable accommodations, and prepare an Academic Accommodation Letter for faculty. To get started, or to re-initiate services, please visit oae.stanford.edu.
    If you already have an Academic Accommodation Letter, please use ( this form ) to upload it and detail the specific accommodations you will need in this course. Letters are preferred by the end of week 2, and at least two weeks in advance of any exam, so we may partner with you and OAE to identify any barriers to access and inclusion that might be encountered in your experience of this course. New accommodation letters, or revised letters, are welcome throughout the quarter; please note that there may be constraints in fulfilling last-minute requests.