Title of the course: Algebraic Curves
Instructor: Dr. Davide Cesare Veniani
Institution: Johannes Gutenberg-Universität Mainz
Dates: 6-12 August 2018
Prerequisites: Basic ring theory (ideals, polynomials, fields, algebraic closure)
Level: Graduate, advanced undergraduate, beginning undergraduate
Abstract: This course is intended as an invitation to algebraic geometry. The theory of algebraic curves already shows many of the complexities of this field, but it is an accessible topic that will help the students build a strong intuition. The main focus will be on affine and projective plane curves, but we will also develop fundamental algebraic tools such as Hilbert’s Nullstellensatz and discrete valuation rings. Our main result will be Bézout’s Theorem. This course will be a complement to Dino Festi’s course on elliptic curves.
Textbook or/and course webpage: “Algebraic Curves” by W. Fulton, chapters 1-5