Asian Journal of Mathematics

Volume 19 (2015)

Number 2

Normal crossing singularities and Hodge theory over Artin rings

Pages: 235 – 250



Christian Lehn (Institut für Algebraische Geometrie, Gottfried Wilhelm Leibniz Universität, Hannover, Germany)


We introduce the notion of a mixed Hodge structure over an Artin ring, thereby establishing a framework for applying Hodge theoretic arguments to deformation problems. Examples arise from relative simple normal crossing varieties over Artinian base schemes. As an application we prove that the maps between graded pieces of Hodge bundles have constant rank.


deformations, local triviality, Hodge theory, normal crossings

2010 Mathematics Subject Classification

13D10, 14C30, 32S35

Published 25 March 2015