Algebraic surface

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

[edit intro]

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[edit]

## Classification[edit]

### Invariants[edit]

* classical invariants
* the Kodaira dimension

### The Picard group and intersection theory[edit]

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

### Negative Kodaira dimension[edit]

### Kodaira dimension 0[edit]

### Kodaira dimension 1[edit]

### General type[edit]

### Positive characteristics[edit]

## References[edit]

* 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