Mumford's influence on the moduli theory of algebraic varieties

2018/09/27 by Kollár, János
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.10723

Abstract

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.

Related

• Mumford divisors
• Moduli theory and arithmetic of algebraic varieties
• Moduli of varieties of general type
• Remark on a theorem in Mumford's Red Book of Varieties and Schemes
• On Hrushovski's proof of the Manin-Mumford conjecture