代数几何 I&II


课程主页 http://www.jliumath.com/teaching/2025fallAG.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S104和S106（二到十周星期四）
上课时间
  • 星期二 13:30-16:10
  • 星期四 13:30-16:10
相关通知
  • 第一次课程的时间为2025年9月23日。
  • 2025年10月2日和2025年10月7日因国庆节放假停课。
课后习题 [习题一]    [习题二]    [习题三]    [习题四]    [习题五]    [习题六]
课程安排
日期 内容 日期 内容
09.23 Sheaves I 09.25 Sheaves II; Afffine algebraic sets
09.30 Affine algebraic variety; Irreducibility; Dimension I 10.09 Dimension II; Zariski tangent spaces; Singularity
10.14 Normality; Prevariety; Separation 10.16 Product; Completeness; Rational functions I
10.21 Rational functions II; Projective variety I 10.23 Projective variety II; Scheme I
10.28 Scheme II 10.30 Scheme III; Vector bundle I
11.04 Vector bundles II 11.06 Locally free sheaves; Divisors I
11.11 Divisors II; Ample line bundles I 11.13 Ample line bundles II
11.18 Ample line bundles III; (Quasi-)coherent sheaves I 11.20 (Quasi-)coherent sheaves II
11.25 (Quasi-)coherent sheaves III; Differentials I 11.27 Differentials II; Derived functors I
12.02 Derived functors II; Formal de Rham Theorem I 12.04 Formal de Rham Theorem II; Cohomologies of affine varities; Cech cohomology I
12.09 Cech cohomologies II; Cohomologies of projective varieties I 12.11 Cohomologies of projective varieties II
12.16 Duality I 12.18 Duality II; Morphisms I
12.23 Morphisms II 12.25 Exam
参考教材
  1. Joseph Le Potier. Goémétrie Algébrique (Note @ Université Denis Diderot-Paris 7) https://www.imj-prg.fr/tga/jlp/coursM2_le_potier.pdf
  2. Mircea Mustață. Introduction to Algebraic Geometry (Note @ University of Michigan). http://www-personal.umich.edu/~mmustata/ag0523.pdf
  3. Andreas Gathmann, Algebraic Geometry (Note @ TU Kaiserslautern) https://agag-gathmann.math.rptu.de/de/alggeom.php
  4. Robin Hartshorne, Algebraic Geometry. Graduate Texts in Mathematics, vol. 52. Springer, New York (1977).