Algebraic surface

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




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


  • 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