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
Chapter 1: Basics on algebraic surfaces
1.1 Cubic surfaces. Note 1, Sep 9
1.2 Curves on surfaces and intersection numbers. Note 2, Sep 16
1.3 Blow-ups, rational maps and linear systems. Note 3, Sep 23
1.4 Structure of birational maps. Note 4, Sep 28
1.5 Exceptional curves, Du Val and rational singularities, singularities of double coverings. Note 5, Sep 30
Chapter 2: Classification theory
2.1 Nakai-Moishezon Criterion, Hodge index theorem and Kodaira dimension. Note 6, Oct 14
2.2 Noether-Enriques theorem, geometrically ruled surfaces and rank 2 vector bundles on curves. Note 7, Oct 21
2.3 Minimal models of ruled surfaces and Castelnuovo's rationality criterion. Note 8, Oct 28
2.4 Morphisms to curves, Zariski lemma and elliptic fibrations. Note 9, Nov 4
2.5 Canonical bundle formula, Kodaira's table of singular fibres and classification of elliptic surfaces. Note 10, Nov 11
2.6 K3 surfaces, curves on K3s, more examples. Note 11, Nov 18
2.7 Enriques surfaces, curves and linear systems on Enriques surfaces. Note 12, Nov 25
2.8 Abelian surfaces, Albanese morphisms, and surfaces with pg=0 and q≥1. Note 13, Dec 2
2.9 Bi-elliptic surfaces. Note 14, Dec 9
Chapter 3: Geography of surfaces of general type
3.1 Some general properties of surfaces of general type. Note 15, Dec 16
3.2 Miyaoka-Yau inequality. Note 16, Dec 16
3.3 Geometry of pluri-canonical maps. Note 17, Dec 16
Chapter 4: Enriques-Kodaira classification via MMP.
4.1 Surfaces with non-nef canonical bundle. Note 18, Dec 23
4.2 Minimal Model Program for surfaces. Note 19 , Dec 23
4.3 Surfaces with Kodaira dimension 0. Note 20, Dec 23
Chapter 5*: Fibrations of algebraic surfaces
5.1 Slope inequality
5.2 Hyperelliptic fibrations
5.3 Canonical fibrations
5.4 Albanese fibrations
5.5 Fibrations of low genus
References:
Algebraic Surfaces, L. Bǎdescu
Complex Algebraic Surfaces, A. Beauville
Compact Complex Surfaces, BHPV
Classification of Complex Algebraic Surfaces, C. Ciliberto
Chapters on Algebraic Surfaces, M. Reid
The fibrations of algebraic surfaces, G. Xiao
Surfaces fibrées en courbes de genre deux, G. Xiao
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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