Lifting of Automorphisms to the normalisation

Question

Let $X$ be a nodal curve, and let $\phi\in Aut(X)$. Let $\tilde{X}$ its normalisation.

Is there a condition on $\phi$ to be lift to $\tilde{X}$?

How about involutions?

Thanks

Answer 1

Normalization is a functor. This means that automorphisms, as well as involutions, lift canonically.