Normal crossing singularities and Hodge theory over Artin rings (Q2348276)

This paper establishes a framework for applying Hodge theoretic arguments to deformation problems. It introduces mixed Hodge structures over an Artin ring \(R\) over \(\mathbb C\). A canonical complex conjugation on \(R\)-modules is obtained using Weil restriction from \(\mathbb C\) to \(\mathbb R\). The author defines an mixed Hodge-Weil structure. The existence of such a structure on cohomology is shown for locally trivial deformations of normal crossings varieties. Some classical results are extended to this setting.