复几何前沿 II


课程主页 http://www.jliumath.com/teaching/2024fallCGII.html
授课教师 刘杰，邮箱地址 : jliu [at] amss.ac.cn
上课地点 中国科学院大学中关村校区N110
上课时间
  • 星期三 10:00-11:40
  • 星期五 13:30-16:10
相关通知
  • 2024年12月01号至2024年12月07号课程暂停一周。
  • 2025年01月01号元旦节课程暂停一次。
课后习题 [习题一]    [习题二]    [习题三]
课程安排
日期 内容 日期 内容
11.08 Complex Manifolds; Vector Bundles I 11.13 Vector Bundles II; Complex Structure
11.15 (Co-)tangent Bundles; Differential Calculus; Sheaf Cohomology I 11.20 Sheaf Cohomology II; Dolbeault Cohomology
11.22 Connection and Hermitian Geometry I 11.27 Connection and Hermitian Geometry II, Line bundle and Divisor I
11.29 Line Bundle and Divisor II, Chern class I 12.11 Chern Class II, Kähler manifold I
12.13 Kähler manifold II 12.18 Hodge theory on Riemannian manifolds
12.20 Hodge theory on Hermitian manifolds; Hodge Theory on Kähler manifolds I 12.25 Hodge theory on Kähler manifolds II
12.27 Lefschetz Theorems; Addendum I 01.03 Addendum II; Kodaira Theorem I
01.08 Kodaira Theorem II 01.10 Final Exam
参考教材
  1. Olivier Biquard and Andreas Höring, Kähler geometry and Hodge theory, 2008. https://math.univ-cotedazur.fr/~hoering/hodge3/hodge.pdf
  2. Jean-Pierre Demailly, Complex analytic and differential geometry, 2012. https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf
  3. Daniel Huybrechts, Complex geometry: an introduction, 2005, Universitext, Springer-Verlag, Berlin.
  4. Claire Voisin, Hodge theory and complex algebraic geometry I & II, Cambridge Studies in Advanced Mathematics, vol. 76 & 77. Cambridge University Press, Cambridge (2003)