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 two, the birational geometry of algebraic surfaces was largely worked out by the Italian school of algebraic geometry in the years 1890-1910. From about 1970 advances have been made in higher dimensions, giving a good theory of birational geometry for dimension three.
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