General base change for relative Du Bois complexes
Caleb Ji, S\'andor Kov\'acs
TL;DR
This paper investigates the behavior of relative Du Bois complexes in families parametrized by a curve, showing they generally commute with base change at general points but often fail at special points.
Contribution
It provides a partial answer to a question about base change properties of relative Du Bois complexes and clarifies when this property holds or fails.
Findings
Relative Du Bois complexes commute with base change at general points.
The property usually fails at special points.
Partial resolution of a question by Kovács and Taji.
Abstract
A partial answer is given to a question raised by Kov\'acs and Taji in arxiv:2307.07192, namely that the relative Du Bois complex of a family parametrized by a non-singular curve commutes with base change to a general point on the base. It is also shown that this property usually fails for special points.
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