On automorphisms of quasi-smooth weighted complete intersections

We show that every reductive subgroup of the automorphism group of a quasi-smooth well-formed weighted complete intersection of dimension at least $3$ is a restriction of a subgroup in the automorphism group in the ambient weighted projective space. Also, we provide examples demonstrating that the automorphism group of a quasi-smooth well-formed Fano weighted complete intersection may be infinite and even non-reductive.
Bibliography: 25 titles.