Birational geometry

In mathematics, birational geometry is a part of the subject of algebraic geometry, that deals with the geometry of an algebraic variety that is dependent only on its function field. In the case of dimension 2, the birational geometry of algebraic surfaces was largely worked out by the Italian school of algebraic geometry in the two decades on either side of the year 1900. From about 1970 advances have been made in higher dimensions, giving a good theory of birational geometry for dimension 3.

See also

• Birational invariant
• Blowing up