Asian Journal of Mathematics

Volume 23 (2019)

Number 2

Automorphism groups of smooth quintic threefolds

Pages: 201 – 256



Keiji Oguiso (Mathematical Sciences, University of Tokyo, Japan; and Korea Institute for Advanced Study, Seoul, South Korea)

Xun Yu (Center for Applied Mathematics, Tianjin University, Tianjin, China)


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.


automorphisms, quintic threefolds, hypersurfaces, finite groups

2010 Mathematics Subject Classification

14J32, 14J50, 14J70, 20E99

Dedicated to Professor Shigeru Mukai on the occasion of his sixtieth birthday

The first author is supported by JSPS Grant-in-Aid (S) No 25220701, JSPS Grant-in-Aid (S) No 22224001, JSPS Grant-in-Aid (B) No 22340009, and by KIAS Scholar Program.

Received 5 December 2016

Accepted 16 August 2017

Published 28 June 2019