Automorphisms of weighted projective hypersurfaces

We prove several results concerning automorphism groups of quasismooth complex weighted projective hypersurfaces; these generalize and strengthen existing results for hypersurfaces in ordinary projective space. First, we prove in most cases that automorphisms extend to the ambient weighted projective space. We next provide a characterization of when the linear automorphism group is finite and find an explicit uniform upper bound on the size of this group. Finally, we describe the automorphisms of a generic quasismooth hypersurface with given weights and degree.