Abstract
Let K be the function field of a variety of dimension greater than or equal to 2 over an algebraically closed field of characteristic zero. Then Hilbert's tenth problem for K is undecidable. This generalizes the result by Kim and Roush, 1992, that Hilbert's tenth problem for the purely transcendental function field ℂ(t 1 ,t 2 ) is undecidable.
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