**What is the automorphisms group of the weighted projective space $\mathbb{P}(a_{0},...,a_{n})$ ?**
Consider the simplest case of a weighted projective plane, take for instance $\mathbb{P}(2,3,4)$; any automorphism has to fix the two singular points. Consider a smooth point $p\in\mathbb{P}(2,3,4)$. **What is the subgroup of the automorphisms of $\mathbb{P}(2,3,4)$ fixing $p$ ?**