Algebraic surface

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

Classification

Invariants

• classical invariants
• the KOdiara dimension

The Picard group and intersection theory

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

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