# Are there only finitely varieties of general type dominated by a given variety in the following sense

Let $X$ be a smooth projective complex algebraic variety. I believe the answer to the following question should be well-known. It is an instance of the Iitaka conjecture.

There are only finitely many isomorphism classes of smooth projective varieties of general type $Y$ such that there exists a surjective proper birational morphism from $X$ to $Y$.

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