Reference that the blow-up of a smooth variety along a smooth subvariety is smooth. Accoding to this post: > The blow-up of a non-singular variety along a non-singular subvariety is well-known to be non-singular Is that difficult, or rather trivial? In the latter case, what is a hint to solve it? If its difficult, what is a reference? I scanned Hartshorne, Chapter II 7, where the general blow-up is defined, but I didn't find anything.

This is **Theorem II 8.24** in Hartshorne's _Algebraic Geometry_.