Ma125 - Algebraic Curves (Spring 2026)

InstructorYassine El Maazouz
Course Webpage http://www.yelmaazouz.org/Ma125/index.html
Course Code Ma125
LecturesTu-Th 13:00–14:25, classroom: TBD
E-Mail:maazouz [at] caltech [dot] edu
Office HoursFridays 14:30-15:30
Excluding holidays. Please email me if you cannot make any of these times.
PrerequisitesA foundation in Abstact Algebra (Ma 5/105 abc, preferably Ma 120 abc) and Complex Analysis Ma 110 abc. Familiarity with ideals of polynomials and basics of affine and projective algebraic varieties would be helpful.
Required Text References : Notes from the lectures will be uploaded below. We will not follow exactly any reference, but we will get inspiration from:
  1. W. Fulton, Algebraic Curves. Available online.
  2. A. Gathmann, Plane algebraic curves. Available online.
  3. R. Miranda, Algebraic Curves and Riemann Surfaces. American Mathematical Society.
  4. R. Cavalieri und E. Miles, Riemann Surfaces and Algebraic Curves. Cambridge University Press.
  5. F. Kirwan, Complex Algebraic Curves. Cambridge University Press.
  6. D. Eisenbud, J. Harris, The Practice of Algebraic Curves: A Second Course in Algebraic Geometry .
  7. E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris, Geometry of Algebraic Curves, Volume I.
Course Description Topics to be covered will include.
  1. Basic foundations of affine and projective geometry.
  2. Affine Plane Curves and local properties.
  3. Projective Curves and Bézout’s theorem.
  4. Function Fields, Rational Functions and Birational equivalence.
  5. Singularities and Resolutions.
  6. Divisors and Linear Systems.
  7. Riemann–Roch Theory.
  8. Genus and Classification.
  9. Morphisms and Maps Between Curves.
  10. Complex algebraic curves as Riemann surfaces.
Homework There will be weekly problem sets. Collaboration (between students) on homework is encouraged. It is important to make sure you understand the solutions yourself, so you are required to write your own solutions separately. I also strongly recommend that you spend some time attempting the problems yourself first before discussing with someone else. You are required to name all your collaborators. You can use any result discussed in the lectures.
DO NOT PLAGIARIZE! The use of AI chatbots on problem sets is completely forbidden.
Please write clear and legible solutions. It is strongly recomemded to write your solutions in TeX.
Homework is due on Fridays at 23:59 PST and is to be submitted on Gradescope.
Late homework submissions will not be accepted.
Final Exam There will be a take-home final exam at the end of the term. The exact date will be announced later on.
Grading The final grade will be based 60% on the problem sets and 40% on the final exam. The lowest homework grade will be dropped.