Algebraic surfaces (代数曲面)

Teaching information

Instructor: 杜佳宾（Jiabin DU）

Email: jiabin.du@simis.cn

Office: SIMIS 1619

Course information:

Course time: every Tuesday 9:55-12:30 a.m., at SIMIS 1610

Pre-requisite Courses

Commutative Algebra, Algebraic Geometry

Syllabus

Week 1-5

Goal: Basics on algebraic surfaces



1. Cubic surfaces, rational scrolls
2. Curves on surfaces and intersection numbers
3. Surfaces and singularities

Week 6-9

Goal: Classification theory



1. Positivity of divisors
2. Enriques-Kodaira classification on surfaces

Week 10-12

Goal: Fibrations of algebraic surfaces



1. Slope inequality
2. Genus two fibrations
3. Hyperelliptic fibrations
4. Canonical fibrations
5. Albanese fibrations
6. Fibrations of low genus

Week 13-16

Goal: Geography of surfaces of general type



1. Miyaoka-Yau inequality
2. Noether and Debarre inequalities
3. Castelnuovo inequality
4. Severi and Barja-Pardini-Stoppino inequalities
5. Geometry of pluri-canonical maps
6. Classification of surfaces with small invariants

References:

1. Chapters on Algebraic Surfaces, M. Reid
2. Complex Algebraic Surfaces, A. Beauville
3. Compact Complex Surfaces, BHPV
4. The fibrations of algebraic surfaces, G. Xiao
5. Surfaces fibrées en courbes de genre deux, G. Xiao
6. Works of A. Beauville, F. Catanese, O. Debarre, E. Horikawa, G. Xiao, X. Lv-K. Zuo, M. Barja, R. Pardini, L. Stoppino and etc

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