2017 Advanced topics in Analysis C1

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Honda Nobuhiro 
Course component(s)
Lecture     
Day/Period(Room No.)
Fri3-4(H137)  
Group
-
Course number
MTH.C407
Credits
1
Academic year
2017
Offered quarter
3Q
Syllabus updated
2017/8/28
Lecture notes updated
-
Language used
Japanese
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Course description and aims

Basic materials on compact Kaehler manifolds will be explained.

Student learning outcomes

To understand special properties on cohomology groups on compact Kahler manifolds, as well as their proofs.

Keywords

Kahler metric, Kahler manifold, Hodge decomposition, Kahelr identity, Lefschetz decomposition, primitive cohomology, Hodge index theorem, divisors and line bundles

Competencies that will be developed

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

Class flow

Standard course

Course schedule/Required learning

  Course schedule Required learning
Class 1 Kahler manifolds and examples Details will be provided during each class session
Class 2 Hodge decomposition
Class 3 Kahler identity
Class 4 primitive cohomology
Class 5 Lefschetz decomposition
Class 6 index formula
Class 7 divisors and line bundles
Class 8 Picard groups and Chern classes

Textbook(s)

None

Reference books, course materials, etc.

P. Griffiths, J. Harris, "Principles of Algebraic Geometry", Wiley-Interscience
R.O.Wells, Differential analysis on complex manifolds, Springer GTM 65

Assessment criteria and methods

Assignments (100%).

Related courses

  • MTH.B505 : Advanced topics in Geometry E1
  • MTH.B506 : Advanced topics in Geometry F1

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

none

Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

honda[at]math.titech.ac.jp

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