2024 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry E
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Nobuhiro Honda
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Tue
- Class
- -
- Course Code
- MTH.B501
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
Introduction to complex manifolds. This course will be succeeded by Advanced topics in Geometry F.
Course description and aims
To understand the content covered in the lectures.
Keywords
complex manifold, divisor and linear system, sheaf cohomology group, blowup
Competencies
- 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/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Introduction to complex manifolds, projective space |
Details will be provided during each class |
| Class 2 | holomorphic mapping, tangent space, differential forms |
Details will be provided during each class |
| Class 3 | holomorphic line bundle, divisor, linear system |
Details will be provided during each class |
| Class 4 | intersection number |
Details will be provided during each class |
| Class 5 | sheaf and cohomology group |
Details will be provided during each class |
| Class 6 | blowup |
Details will be provided during each class |
| Class 7 | resolution of singularity |
Details will be provided during each class |
Study advice (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）
Evaluation methods and criteria
Graded by homeworks.
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- MTH.B331 ： Geometry III
- MTH.B341 ： Topology
Prerequisites
At least, knowledge of undergraduate calculus and linear algebra, as well as differential manifolds are required.