2021 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry H1
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Nobuhiro Honda
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Fri
- Class
- -
- Course Code
- MTH.B508
- Number of credits
- 100
- Course offered
- 2021
- Offered quarter
- 4Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
Theory of K3 surfaces are treated. K3 surfaces are compact simply connected Kaehler surface with vanishing Ricci curvature,
and play significant role in complex geometry. This course succeeds Advanced topics in Geometry G1 in 3Q.
Course description and aims
To understand that a large part of the theory of K3 surfaces are dominated by second cohomology groups.
Keywords
K3 surface, Kummer surface, K3 lattice, Hodge isometry, Torelli theorem, Kaehler 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
regular lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Definition and fundamental properties of K3 surfaces, examples | Definitions and properties |
| Class 2 | Kummer surfaces | Definitions and properties |
| Class 3 | Torelli theorem on K3 surfaces | Definitions and properties |
| Class 4 | moduli space of marked K3 surfaces, 1 | Definitions and properties |
| Class 5 | moduli space of marked K3 surfaces, 2 | Definitions and properties |
| Class 6 | local Torelli theorem | Definitions and properties |
| Class 7 | polarized K3 surfaces and period domain | Definitions and properties |
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)
No textbook
Reference books, course materials, etc.
Barth, Hulek, Peters and van de Ven, "Compact complex surfaces", Springer
D. Huybrechts, "Lectures on K3 surfaces", Cambridge University Press
Evaluation methods and criteria
based on homework assignments
Related courses
- MTH.B202 ： Introduction to Topology II
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
Prerequisites
Assumed to have taken Advanced topics in Geometry G1 in 3Q.