Good morning,

I would like to ask the following question concerning the desingularisation, but I'm not familiar at all with these notions.

We have the following theorem of Hironaka: Let $X\subset \mathbb{CP}^n$ a closed complex projective variety. Then, there exists a modification $f\colon (\tilde{X},E) \to (X, Sing(X))$ such that $\tilde{X}$ is smooth and projective, and the exceptional divisor $E$ is a divisor with normal crossings.

**My questions:** Are $f$ and $f^{-1}$ rational maps?

Any help is appreciated. Thanks in advance,

Duc Anh