Algebraic surface

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

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. ${\displaystyle p}$; 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