On automorphisms of quasi-smooth weighted complete intersections

TL;DR

This paper investigates the automorphism groups of quasi-smooth weighted complete intersections, showing restrictions of automorphisms from ambient spaces and providing examples of infinite, non-reductive automorphism groups.

Contribution

It establishes that reductive automorphisms are restrictions from ambient spaces and presents examples of complex automorphism group structures.

Findings

Reductive subgroups are restrictions from ambient space automorphisms.

Automorphism groups can be infinite and non-reductive.

Examples illustrate diverse automorphism group behaviors.

Abstract

We show that every reductive subgroup of the automorphism group of a quasi-smooth well formed weighted complete intersection is a restriction of a subgroup in the automorphism group in the ambient weighted projective space. Also, we provide examples demonstrating that an automorphism group of a quasi-smooth well formed Fano weighted complete intersection may be infinite and even non-reductive.