Algebraic Curves
This course offers a concise introduction to algebraic curves using Fulton's classic text. Starting with affine and projective varieties, we cover Hilbert's Basis Theorem and Nullstellensatz to establish the algebra-geometry correspondence. From there, we study plane curves and intersection theory, proving Bézout's Theorem. The main goal is the Riemann-Roch Theorem, developed through divisors, differentials, and genus. Applications include elliptic curves and an introduction to the Riemann zeta function for function fields over finite fields.
Lecturer
Date
10th March ~ 2nd June, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 10:40 - 12:15 | A14-203 | ZOOM A | 388 528 9728 | BIMSA |
| Tuesday | 14:20 - 16:05 | A14-203 | ZOOM A | 388 528 9728 | BIMSA |
Prerequisite
A solid grounding in abstract algebra is required, including rings, ideals, fields, and modules. Familiarity with Galois theory, particularly finite field extensions and their automorphism groups, is expected. Some exposure to point-set topology and complex analysis is helpful but not strictly necessary.
Reference
Fulton, William. Algebraic Curves: An Introduction to Algebraic Geometry. (Primary text)
Silverman, Joseph H. The Arithmetic of Elliptic Curves.
Rosen, Michael. Number Theory in Function Fields. Springer, 2002 . (Provides the analytic and arithmetic perspective on function fields, connecting to the zeta function discussed in the course.)
Silverman, Joseph H. The Arithmetic of Elliptic Curves.
Rosen, Michael. Number Theory in Function Fields. Springer, 2002 . (Provides the analytic and arithmetic perspective on function fields, connecting to the zeta function discussed in the course.)
Audience
Advanced Undergraduate
, Graduate
Video Public
Yes
Notes Public
Yes
Language
Chinese
, English
Lecturer Intro
2010-2014年，就读于南开大学，获得理学学士学位；
2014-2021年，就读于中国科学院数学与系统科学研究院，获得理学博士学位；
2021-2024年，就职于北京雁栖湖应用数学研究院做博士后；
2024年至今，就职于北京雁栖湖应用数学研究院，职位是Assistant Professor in Practice
2014-2021年，就读于中国科学院数学与系统科学研究院，获得理学博士学位；
2021-2024年，就职于北京雁栖湖应用数学研究院做博士后；
2024年至今，就职于北京雁栖湖应用数学研究院，职位是Assistant Professor in Practice