Birational invariant

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In algebraic geometry, a birational invariant is a quantity or object that is well-defined on a birational equivalence class of algebraic varieties. In other words, it depends only on the function field of the variety.

For example in the case of an algebraic surface, the Hodge numbers h^0,1 and h^0,2 of a non-singular projective complex surface are birational invariants. The Hodge number h^1,1 is not, since the process of blowing up a point to a curve on the surface can augment it.

[edit] External links

• A birational invariant for algebraic group actions