Mumford’s influence on the moduli theory of algebraic varieties

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.

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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