2017 Advanced courses in Algebra A

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Academic unit or major
Mathematics
Instructor(s)
Ma Shohei 
Course component(s)
Lecture
Day/Period(Room No.)
Thr5-6(H137)  
Group
-
Course number
ZUA.A331
Credits
1
Academic year
2017
Offered quarter
1Q
Syllabus updated
2017/3/17
Lecture notes updated
-
Language used
Japanese
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Course description and aims

We study algebraic curves. The basic results are the Rieman Roch theorem, Hodge decomposition and the canonical model.

Student learning outcomes

Being familiar with Riemann-Roch

Keywords

curves, Riemann surfaces

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Standard lecture course

Course schedule/Required learning

  Course schedule Required learning
Class 1 curves Details will be provided during each class session
Class 2 sheaves Details will be provided during each class session
Class 3 cohomology Details will be provided during each class session
Class 4 Riemann-Roch
Class 5 Duality Details will be provided during each class session
Class 6 canonical model Details will be provided during each class session
Class 7 Hodge decomposition Details will be provided during each class session
Class 8 Jacobian Details will be provided during each class session

Textbook(s)

None required

Reference books, course materials, etc.

E.Arbarello, M.Cornalba, P.Griffiths, J.,Harris, `Geometry of Algebraic Curves I' Springer.
R.Narashimhan, `Compact Riemann surfaces'
J.Harris, I.Morrison, `Moduli of Curves' Springer

Assessment criteria and methods

Depends on the report (100%). Details will be announced during the course.

Related courses

  • ZUA.A332 : Advanced courses in Algebra B

Prerequisites (i.e., required knowledge, skills, courses, etc.)

None required

Other

Do not hesitate to ask any question

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