2017 Advanced topics in Analysis D1

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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.C408
Credits
1
Academic year
2017
Offered quarter
4Q
Syllabus updated
2017/9/22
Lecture notes updated
-
Language used
Japanese
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Course description and aims

This course is a succession of MTH.C407. Basic materials on compact Kaehler manifolds will be explained.

Student learning outcomes

Students are expected to learn
・representation of Chern classes in terms of curvature forms,
・vanishing theorem of cohomology groups under positivity condition of curvature
・computations of numerical invariants of simple algebraic varieties

Keywords

connection and curvature, Chern classes, vanishing theorem, hyperplane theorem, adjunction formula

Competencies that will be developed

Specialist skills Intercultural skills Communication 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 connection of complex vector bundles Details will be provided during each class session
Class 2 Chern classes of holomorphic line bundles
Class 3 geometric interpretation of Chern classes
Class 4 vanishing theorem
Class 5 application of vanishing theorem
Class 6 adjunction formula and its application
Class 7 numerical invariant of algebraic surfaces

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.C407 : Advanced topics in Analysis C1
  • MTH.B505 : Advanced topics in Geometry E1
  • MTH.B506 : Advanced topics in Geometry F1

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

none

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