Automorphism groups of smooth quintic threefolds

TL;DR

This paper classifies all maximal automorphism groups of smooth quintic threefolds, providing explicit examples and identifying exactly 22 such groups, advancing understanding of symmetries in algebraic geometry.

Contribution

It explicitly describes all maximal automorphism groups of smooth quintic threefolds, identifying exactly 22 such groups with concrete examples.

Findings

22 maximal automorphism groups identified

Explicit examples of target quintic threefolds provided

Complete classification of these groups achieved

Abstract

We study automorphism groups of smooth quintic threefolds. Especially, we describe all the maximal ones with explicit examples of target quintic threefolds. There are exactly $22$ such groups.