Algebraic surface: Difference between revisions

Revision as of 12:37, 17 March 2007

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

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

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 === Examples ===
-=== Classification ===
+== Classification ==
-== Invariants ==
+=== Invariants ===
+* classical invariants
-== The Picard group ==
+* the KOdiara dimension
+=== The Picard group and intersection theory ===
-== Negative Kodaira dimension ===
+* intersection product
-== Kodaira dimension 0 ===
+* various forms of Riemann Roch
-== Kodaira dimension 1 ===
+* kodaira dimension
-== Kodaira dimension 2 ===
+=== Negative Kodaira dimension ===
+=== Kodaira dimension 0 ===
+=== Kodaira dimension 1 ===
+=== General type ===
+=== Positive characteristics ===
 == References ==
-*A. Beauville Complex algebraic surfaces ISBN 0521498422
+*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
 [[Category:Mathematics Workgroup]]
 [[Category:CZ Live]]