Math 601M: Algebraic Geometry

Syllabus: Basic concept about compact Riemann Surface. We start by talking about basic concept about the complex projective space,

characteristic derivative, simple examples of Riemann Surface, and so on. Next we are going to talk about Riemann-Roch Theorem, its applications and its proof; Hodge Theorem and its proof. In between, we will talk about some important definitions and lemmas such as factor, Dolbeault lemma and so on.

Text: Introduction to compact Riemann surface, by Hu(1981) [Chinese version]

Instructor: Dr. Wei Pei Li

Syllabus:

(Before Lesson 1, read appendix 1 and 2)

Lesson 1: Chapter 1.1

Lesson 2: 1.2

Lesson 3: 1.3

Lesson 4: 1.3

Lesson 5:1.4

Lesson 6: Presentation on chapter 1.

Lesson 7: 2.5

Lesson 8:2.6

Lesson 9: 2.6

Lesson 10:2.6

Lesson 11:2.6

Lesson 12: Revision of chapter 2.

Lesson 13: Presentation of chapter 1 and 2.

-         Presentation to Dr. Li.

Lesson 14: 3.7

Lesson 15: 3.7

Lesson 16: 3.7

Lesson 17: 3.7

Lesson 18: 3.8

Lesson 19: 3.8

Lesson 20: 3.8

Lesson 21: Presentation of 3.7 and 3.8

Lesson 22: 3.9

Lesson 23: 3.9

Lesson 24: 3.9

Lesson 25:3.9

Lesson 26: 3.9

Lesson 27: Presentation of 3.9

-         Presentation to Dr. Li

Lesson 28: 3.10

Lesson 29: 3.10

Lesson 30: 3.10

Lesson 31: 3.10

Lesson 32: 3.10

Lesson 33: Presentation of 3.10

Lesson 32: 3.11

Lesson 33: 3.11

Lesson 34: 3.11

Lesson 35: 3.11

Lesson 36: 3.11

Lesson 37: Presentation of 3.11

-         Presentation to Dr. Li

Lesson 38: 3.12

Lesson 39: 3.12

Lesson 40: 3.12

-         Presentation to Dr. Li

If the above schedule is followed successfully, we will go on chapter 4 and 5.

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