Pure and Applied Mathematics Quarterly

Volume 17 (2021)

Number 2

Special Issue: In Honor of David Mumford

Guest Editors: Ching-Li Chai, Amnon Neeman

Mumford’s influence on the moduli theory of algebraic varieties

Pages: 619 – 647

DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n2.a3


János Kollár (Department of Mathematics, Princeton University, Princeton New Jersey, U.S.A.)


We give a short appreciation of Mumford’s work on the moduli of varieties by putting it into historical context. By reviewing earlier works we highlight the innovations introduced by Mumford. Then we discuss recent developments whose origins can be traced back to Mumford’s ideas.

Partial financial support was provided by the NSF under grant number DMS-1362960.

Received 27 September 2018

Accepted 8 November 2018

Published 12 May 2021