In algebraic geometry, a **birational invariant** is a property of a variety (or more generally, an algebraic scheme) that remains unchanged under birational equivalence. Two varieties \( X \) and \( Y \) are said to be birationally equivalent if there exist rational maps from \( X \) to \( Y \) and from \( Y \) to \( X \) that are inverses of each other on a dense open subset of each variety.
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