2026 (Current Year) Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry H
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Nobuhiro Honda
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- MTH.B504
- Number of credits
- 100
- Course offered
- 2026
- Offered quarter
- 4Q
- Syllabus updated
- Mar 5, 2026
- Language
- English
Syllabus
Course overview and goals
This course includes a discussion of K3 surfaces. A K3 surface is characterized as a compact, simply connected, Ricci-flat Kähler complex surface and occupies a central position in complex geometry. The course continues from “Advanced Topics in Geometry G1” offered in the third quarter.
Course description and aims
To understand the role played by the second cohomology group in the theory of K3 surfaces.
Keywords
K3 surface, Kummer surface, K3 lattice, Hodge isometry, Torelli theorem, Kähler cone, period map, period domain, polarized K3 surface, Weyl group, nodal class
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | K3 surface - definition, basic properties and examples |
Details will be provided in class. |
| Class 2 | Kummer surface |
Details will be provided in class. |
| Class 3 | Torelli theorem |
Details will be provided in class. |
| Class 4 | the moduli spac of marked K3 surface 1 |
Details will be provided in class. |
| Class 5 | the moduli spac of marked K3 surface 2 |
Details will be provided in class. |
| Class 6 | local Torelli |
Details will be provided in class. |
| Class 7 | polarized K3 surface and period domain |
Details will be provided in class. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None
Reference books, course materials, etc.
D. Huybrecht, Lectures on K3 surfaces, Cambridge University Press
Evaluation methods and criteria
Homework assignments (100％)
Related courses
- MTH.B202 ： Introduction to Topology II
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- MTH.B341 ： Topology
- MTH.B503 ： Advanced topics in Geometry G
Prerequisites
This course assumes prior completion of “Advanced Topics in Geometry G1” offered in the third quarter.
Other
To be announced.