Editing Birational geometry (section)

{{Short description|Field of algebraic geometry}}
[[Image:Stereoprojzero.svg|thumb|right|The [[circle]] is birationally equivalent to the [[real line|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 [[Map (mathematics)|mappings]] that are given by [[rational functions]] rather than [[polynomials]]; the map may fail to be defined where the rational functions have poles.