**Title of the course:** An Introduction to Algebraic Curves

**Instructor’s Name:** Prof. Ali Sinan Sertöz

**Institution:** Bilkent U.

**Dates:** 10-14 August 2020

**Prerequisites:** A nodding acquaintance with complex numbers, functions and vector spaces may be helpful. However a certain degree of curiosity and eagerness to learn and an altruistic quest for knowledge, though not officially required, will be extremely useful in extracting a joy of discovery from the course material.

**Level:** Advanced undergraduate

**Abstract:** We will introduce the concept of compact complex curves, otherwise known as compact Riemann surfaces, as opposed to the more friendly and easily understood concept of algebraic curves who live happily in projective spaces. We will see immediately that every smooth complex algebraic curve is a compact Riemann surface but the converse is one of the biggest and earliest achievements of algebraic geometry. It is the famous Riemann-Roch theorem which shows how to embed a compact Riemann surface into a projective space as a smooth algebraic curve. We will describe, and illustrate with ample examples, all these terms as they appear in the course. Besides the Riemann-Roch theorem we will have a chance to meet Bezout’s theorem, Riemann-Hurwitz formula, degree-genus formula, Abel-Jacobi theorem and even a taste of the Torelli theorem which has extensions to K3 surfaces (which we may study some other year).**
Language:** English (mostly!)

Textbook: