Complex Algebraic Surfaces (Spring 2025)

 

What is this course about?

I will give a basic introduction to the theory of complex algebraic surfaces, with the goal of understanding Enriques' classification of surfaces.​

 

Prerequisite

Basic knowledge of algebraic varieties.

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Literature

[1] Arnaud Beauville, Complex Algebraic Surfaces.

[2] Miles Reid, Chapters on Algebraic Surfaces.

[3] Wolf Barth, Klaus Hulek, Chris Peters, Antonius Van de Ven, Compact Complex Surfaces.

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Place and time

Tuesdays, 08:50-12:15; Venue: A3-1a-204

Zoom: 435 529 7909, PW: BIMSA

Starting from Mar. 4

 

WeChat Group

We have created a WeChat Group for communication​. You could write to me if you would like to join.

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Material covered

Mar. 4: Introduction to Enriques-Kodaira classification of surfaces; sheaves.

Mar. 11: Coherent cohomology.

Mar. 18: The Picard group.

Mar. 25: Birational maps.

Apr. 1: Ruled surfaces.

Apr. 8: Ruled surfaces (continued).

Apr. 15: Rational surfaces.

Apr. 22: Castelnuovo's rationality criterion.

Apr. 29: Surfaces with p_g=0 and q>=1.

May 6: Surfaces with \kappa=0.

May 13: Surfaces with \kappa=1.

May 20: Surfaces of general type.

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