MAT 248A, Winter 2024

Instructor

Instructor: Eugene Gorsky, egorskiy AT math.ucdavis.edu.
Office hours: Fridays 1-2pm in Math 2113.
If you have a question and cannot come at office hours, write me an email to schedule an appointment.

Textbook and reading materials

The main textbook for the course is "Algebraic Geometry" by Robin Hartshorne.

Additional reading:
  1. Lecture notes by Brooke Ullery.
  2. Algebra and Geometry by Emily Clader and Dustin Ross.
  3. Undergraduate Algebraic Geometry by Miles Reid.
  4. The Rising Sea by Ravi Vakil.
  5. Krull Dimension and Transcendence Degree. Chapter 5 from "A course in commutative algebra" by Gregor Kemper.
  6. Algebraic Varieties by Brian Osserman.
  7. Algebraic Curves by William Fulton.

Final grade

The grade will be 100% based on the homeworks, the lowest homework score is dropped. There will be no midterms or final exam.

Homework

HW 1 , HW 2, HW 3 , HW 4 , HW 5 , HW 6 , HW 7 , HW 8

Program and lecture notes

1. Algebraic sets, affine varieties and ideals. Lec1

2. Nullstellensatz, irreducibility and prime ideals. Lec2 , Lec3 , Lec4

3. Noetherian rings, Hilbert Basis Theorem Lec5 , Lec6

4. Zariski topology Lec7 , Lec8

5. Rings of functions, morphisms, rational maps. Lec9 , Lec10 , Lec11 , Lec12

5a. Example: blow-up Lec13

5b. Line bundles and maps to projective space: Lec14 , Lec15 , Lec16

6. Dimension and transcendence degree Lec17 , Lec18 , Lec19

7. Zariski tangent space, nonsingular varieties, Bertini's Theorem Lec20 , Lec21 , Lec22

8. Differentials, geometric genus. Lec23 , Lec24 , Lec25 .

9. Divisors, divisor class group. Lec26 , Lec27 , Lec28 .

Disability Services

Any student with a documented disability who needs to arrange reasonable accommodations must contact the Student Disability Center (SDC). Faculty are authorized to provide only the accommodations requested by the SDC. If you have any questions, please contact the SDC at (530)752-3184 or sdc@ucdavis.edu.