# Algebraic surface

Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
Citable Version  [?]

This editable Main Article is under development and subject to a disclaimer.

An algebraic surface over a field ${\displaystyle K}$ is a two dimensional algebraic variety over this field.

## Classification

### 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. ${\displaystyle p}$; 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