Algebraic surface: Difference between revisions
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An '''algebraic surface''' over a [[field]] <math>K</math> is a two dimensional algebraic variety over this field. | An '''algebraic surface''' over a [[field]] <math>K</math> is a two dimensional algebraic variety over this field. | ||
=== Examples === | === Examples === | ||
== Classification == | |||
== Invariants == | === Invariants === | ||
* classical invariants | |||
* the [[Kodaira dimension]] | |||
== The Picard group == | === The Picard group and intersection theory === | ||
* intersection product | |||
== Negative Kodaira dimension === | * various forms of Riemann Roch | ||
== Kodaira dimension 0 === | * kodaira dimension | ||
== Kodaira dimension 1 === | === Negative Kodaira dimension === | ||
== | === Kodaira dimension 0 === | ||
=== Kodaira dimension 1 === | |||
=== General type === | |||
=== Positive characteristics === | |||
== References == | == References == | ||
*W. Barth, C. Peters, and A. Van de Ven ''Compact Complex Surfaces'' | |||
*W. Barth, C. Peters, and A. Van de Ven Compact Complex Surfaces | *A. Beauville ''Complex algebraic surfaces'' ISBN 0521498422 | ||
*P. Griffithis and J. Harris Principles of Algebraic Geometry. Chapter 4 | *E. Bombieri and D. Mumford ''Enriques' classification of surfaces in char. <math>p</math>''; 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 | |||
Latest revision as of 16:33, 1 December 2008
An algebraic surface over a field is a two dimensional algebraic variety over this field.
Examples
Classification
Invariants
- classical invariants
- the Kodaira 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. ; 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
