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Algebraic Curves (BM)


Admission requirements

Algebra 2 (or equivalent background in polynomials, rings and ideals)


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.


You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

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.

Reading list

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.


From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.

Extensive FAQ's on MyStudymap can be found here.