Automorphisms of weighted projective hypersurfaces

Abstract

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 establish a Grothendieck-Lefschetz type theorem for these hypersurfaces. We next provide a characterization of when their linear automorphism group is finite and find explicit uniform upper bounds on the size of this group. Finally, we describe the automorphisms of a generic quasismooth hypersurface with given weights and degree.