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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Honda Nobuhiro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Fri5-6()
- Group
- -
- Course number
- MTH.B508
- Credits
- 1
- Academic year
- 2021
- Offered quarter
- 4Q
- Syllabus updated
- 2021/3/19
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
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.
Student learning outcomes
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 that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
regular lecture course
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| 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 |
Out-of-Class Study Time (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
Assessment criteria and methods
based on homework assignments
Related courses
- MTH.B202 ： Introduction to Topology II
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Assumed to have taken Advanced topics in Geometry G1 in 3Q.
