2024 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry F
- 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.B502
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
Introduction to the theory of rational surfaces. This course is continued from Advanced topics in Geometry E.
Course description and aims
To fully understand the content covered in the lectures.
Keywords
rational surface, relatively minimal model, quadric surface, cubic surface
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 | rational surfaces, examples | Details will be provided during each class session. |
| Class 2 | fibration structure over curve | Details will be provided during each class session. |
| Class 3 | minimal model and relatively minimal model | Details will be provided during each class session. |
| Class 4 | structure of P^1-bundle, ruled surface | Details will be provided during each class session. |
| Class 5 | quadric surfaces | Details will be provided during each class session. |
| Class 6 | cubic surfaces | Details will be provided during each class session. |
| Class 7 | 6 points blowup of P^2, 27 bitangents | Details will be provided during each class session. |
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.B501 ： Advanced topics in Geometry E
Prerequisites
Students are expected to be familiar with the topics treated in Advanced Topics in Geometry E.