This course is a succession of MTH.C407. Basic materials on compact Kaehler manifolds will be explained.
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
connection and curvature, Chern classes, vanishing theorem, hyperplane theorem, adjunction formula
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Standard lecture course
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 |
none
P. Griffiths, J. Harris, "Principles of Algebraic Geometry", Wiley-Interscience
R.O.Wells, Differential analysis on complex manifolds, Springer GTM 65
Assignments (100%).
none