I'm sorry if this is a trivial question, but it seems I can't find a clear answer. 
I have a finitely generated Poisson algebra $A$, the Poisson scheme $X=Spec(A)$ and an automorphism $g$. 


What is the definition of the fixed point subscheme $X^g$?



Fixed point scheme definition
This might be an unhelpful answer, but have you already considered the paper [John Fogarty - Fixed points schemes](https://www.jstor.org/stable/2373642)?


