北京雁栖湖应用数学研究院

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.