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School of Environment and Society
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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 (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Tue3-4(M-B107(H104))
- Group
- -
- Course number
- MTH.B501
- Credits
- 1
- Academic year
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- 2024/3/14
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
Introduction to complex manifolds. This course will be succeeded by Advanced topics in Geometry F.
Student learning outcomes
To understand the content covered in the lectures.
Keywords
complex manifold, divisor and linear system, sheaf cohomology group, blowup
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
A standard lecture course. Homeworks will be assined for each lesson.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Introduction to complex manifolds, projective space | Details will be provided during each class session. |
| Class 2 | holomorphic mapping, tangent space, differential forms | Details will be provided during each class session. |
| Class 3 | holomorphic line bundle, divisor, linear system | Details will be provided during each class session. |
| Class 4 | intersection number | Details will be provided during each class session. |
| Class 5 | sheaf and cohomology group | Details will be provided during each class session. |
| Class 6 | blowup | Details will be provided during each class session. |
| Class 7 | resolution of singularity | Details will be provided during each class session. |
Out-of-Class Study Time (Preparation and Review)
Official Message: 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.
P. Griffiths, J. Harris, "Principles of Algebraic Geometry"（Wiley-Interscience）
Assessment criteria and methods
Graded by homeworks.
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- MTH.B331 ： Geometry III
- MTH.B341 ： Topology
Prerequisites (i.e., required knowledge, skills, courses, etc.)
At least, knowledge of undergraduate calculus and linear algebra, as well as differential manifolds are required.
