## Admission requirements

none

## Description

An introduction to algebraic geometry, concentrating on algebraic curves. Algebraic geometry is the geometric study of solutions to polynomial equations, and has applications throughout mathematics, from number theory to theoretical physics. In this course we will give an introduction focussing on curves (the case of dimension 1). We will study affine and projective algebraic varieties, Hilbert’s Nullstellensatz, the local structure of algebraic curves, divisors, differentials, ...

## Course Objectives

Learn basic foundational results, and combine them with geometric intuition.

## Mode of Instruction

Lectures, exercise classes and homework.

## Assessment method

5 homeworks throughout the semester, or which the best 4 will count (no retakes on homework; they are ‘practicals') for 25%.

Written exam at the end for the other 75%, with a retake which may be written or oral depending on student numbers. Homework also counts for the retake.

The passing grade is 5.5. In addition, you must score at least a 5 on the final exam/retake in order to pass the course.

## Literature

The main reference for the first part of the course will be Introduction to Algebraic Geometry by Igor V. Dolgachev. This book is freely available online, a link will be shared on the Brightspace page.

## Brightspace / website

Brightspace will be used.

## Contact information

holmesdst@math.leidenuniv.nl