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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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Exceptional locus of proper birational morphism from smooth variety to normal variety

Let $f:Y\rightarrow X$ be a proper birational morphism. Suppose that $X$ is normal and $Y$ is smooth. Let us write the largest open subset U of X such that $f^{-1}$ can be defined. I want to show that …