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From Citizendium, the Citizens' Compendium

An algebraic surface over a field K is a two dimensional algebraic variety over this field.

Contents 1 Examples 2 Classification 2.1 Invariants 2.2 The Picard group and intersection theory 2.3 Negative Kodaira dimension 2.4 Kodaira dimension 0 2.5 Kodaira dimension 1 2.6 General type 2.7 Positive characteristics 3 References

Examples

Classification

Invariants

• classical invariants
• the KOdiara dimension

The Picard group and intersection theory

• intersection product
• various forms of Riemann Roch
• kodaira dimension

Negative Kodaira dimension

Kodaira dimension 0

Kodaira dimension 1

General type

Positive characteristics

References

• W. Barth, C. Peters, and A. Van de Ven Compact Complex Surfaces
• A. Beauville Complex algebraic surfaces ISBN 0521498422
• E. Bombieri and D. Mumford Enriques' classification of surfaces in char. p; part I in Global analysis, Princeton university press. Part II in complex analysis and algebraic geometry, Cambridge university press. Part III in Invent Math. 35.
• P. Griffithis and J. Harris Principles of Algebraic Geometry. Chapter 4