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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Yatagawa Yuri
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Mon5-6(M-143B(H119B))
- Group
- -
- Course number
- MTH.A502
- Credits
- 1
- Academic year
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- 2024/3/14
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
Intersection theory is a fundamental theory in algebraic geometry originating from the number of solutions to systems of simultaneous equations, and it serves as a basis for theories such as the theory of motives, which has been rapidly developing in recent years. This lecture aims to study particularly fundamental concepts within intersection theory.
Student learning outcomes
(1) Obtain overall knowledge on basics in intersection theory and become proficient in applying them freely
(2) Attain deep understanding of applications of intersection theory
Keywords
Intersection theory, algebraic cycles, Chow groups, Segre classes, Chern classes
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Segre classes | Details will be provided during each class session |
| Class 2 | Pull-back by regular immersions | Details will be provided during each class session |
| Class 3 | Gysin homomorphism (2) | Details will be provided during each class session |
| Class 4 | Chern classes (2) | Details will be provided during each class session |
| Class 5 | Chern classes (3) | Details will be provided during each class session |
| Class 6 | Intersection products (2) | Details will be provided during each class session |
| Class 7 | Topics on applications | Details will be provided during each class session |
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)
None required.
Reference books, course materials, etc.
W. Fulton, "Intersection Theory, Second Edition, Springer
S. Saito and K. Sato, "Algebraic cycles and Etale cohomologies", Maruzen (Japanese)
Assessment criteria and methods
Course scores are evaluated by homework assignments. Details will be announced during the course.
Related courses
- MTH.A501 ： Advanced topics in Algebra E
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
A basic knowledge of scheme theory at the level of Hartshorne's book is desirable.
Other
None in particular.
