Admission requirements
Algebra 2 (or equivalent background in polynomials, rings and ideals)
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
After this course students will be able to define and use various concepts and tools from affine and projective algebraic geometry over algebraically closed fields. Calculate intersection numbers of algebraic curves with explicit equations.
Timetable
In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.
Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.
Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.
Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.
Mode of Instruction
Lectures, exercise classes and presentation.
Assessment method
Students complete three homework assignments (considered as ‘practical = praktische oefening’), focused on exercises related to—but not covered in—lectures. These test their ability to quickly grasp new concepts and devise correct, creative proofs. Assignments are graded by a TA as usual. A week after grading, a feedback session is held during a scheduled practical. Students with outstanding or original solutions are invited (a week in advance) to present their work to peers; this presentation is not graded but everyone will have to present at least once for a minimum of 20min. These sessions foster discussion and collaborative learning, with lecturers and TAs offering feedback and highlighting common pitfalls. Students who attend all presentation sessions have their assignment grade count for 25% of the final mark; otherwise, it counts for 10%.
The final grade will consist of a combination of homework assignments, written final exam, and (possibly) a resit. The homework grade is the average of all homework grades. There is no retake for the homework.
A minimum homework grade of 5 is required to be admitted to the final or resit exam. If the exam grade is at least 5 then the final grade will be the maximum of the exam grade and the weighted average of exam grade (75% or 90%) and homework grade (25% or 10%, as applicable). If the exam grade is below 5 then the final grade is the exam grade. The same method applies to the resit exam grade. The resit will be written or oral depending on the number of students.
Reading list
The main reference for the first part of the course will be Introduction to Algebraic Curves by Fulton (https://dept.math.lsa.umich.edu/~wfulton/CurveBook.pdf). This book is freely available online, a link will be shared on the Brightspace page. Another excellent reference is Complex Algebraic Curves by Frances Kirwan (https://agorism.dev/book/math/ag/complex-algebraic-curves_francis-kirwan.pdf)
Registration
As a student, you are responsible for enrolling on time through MyStudyMap.
In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.
There are two enrolment periods per year:
Enrolment for the fall opens in July
Enrolment for the spring opens in December
See this page for more information about deadlines and enrolling for courses and exams.
Note:
It is mandatory to enrol for all activities of a course that you are going to follow.
Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.
Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.
Contact
Lecturers:
Dr. Emre Can Sertöz: e.c.sertoz@math.leidenuniv.nl
Dr. Haowen Zhang: h.zhang@math.leidenuniv.nl
Course assistant:
George Politopoulos: g.politopoulos@math.leidenuniv.nl
Remarks
This course is designed to celebrate the technical machinery you've acquired throughout your undergraduate studies in mathematics. Rather than introducing new techniques, we will apply the ones you already know to explore a beautiful and central subject in mathematics: algebraic curves.
Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.