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- Academic unit or major
- Mathematics
- Instructor(s)
- Honda Nobuhiro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- -
- Group
- -
- Course number
- ZUA.E347
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 2Q
- Syllabus updated
- 2018/6/4
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
In this lecture series, we will begin by reviewing some basic material from Kahler geometry. We will then discuss basic examples of Calabi-Yau manifolds, and Yau's Theorem. In dimension 4, these metrics are hyperkahler, and the Gibbons-Hawking ansatz is an important tool for producing noncompact examples, such as ALE, ALF, ALG, ALH, etc. Noncompact examples also arise from a construction of Tian-Yau. We will then outline various gluing results, which give a picture of the degenerations of Yau's metrics on K3 surfaces.
Student learning outcomes
To know some basic concepts of Kahler geometry
To understand basic examples of Calabi-Yau manifolds and hyperkahler metrics on K3 surfaces.
Keywords
Kahler manifold, Calabi-Yau metrics, hyperkahler geometry.
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
standasrd lecture course
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Kahler geometry, basics | Details will be provided during each class session |
| Class 2 | Kahler metrics, Yau's Theorem. | |
| Class 3 | Calabi-Yau manifolds, examples. | |
| Class 4 | Hyperkahler metrics in dimension 4. | |
| Class 5 | Gibbons-Hawking ansatz. | |
| Class 6 | This will be a general colloquium talk about Calabi-Yau metrics on K3 surfaces. | |
| Class 7 | del Pezzo surfaces, rational elliptic surfaces and Tian-Yau Theorem. | |
| Class 8 | Noncompact hyperkahler metrics, ALE, ALF, ALG, ALH. | |
| Class 9 | Nilmanifolds and ALH_b geometry | |
| Class 10 | Examples of collapsing hyperkahler metrics on K3 surfaces. |
Textbook(s)
P. Griffiths, J. Harris, "Principles of Algebraic Geometry", Wiley-Interscience.
Reference books, course materials, etc.
P. Griffiths, J. Harris, "Principles of Algebraic Geometry", Wiley-Interscience.
Assessment criteria and methods
Assignments (100%)
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Basic knowledge on geometry (manifolds, differential forms, homology group) is required.
