Birational geometry

The circle is birationally equivalent to the line. One birational map between them is stereographic projection, pictured here.

In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles.


Birational geometry

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