A short note on Du Bois singularities
Pat Lank
TL;DR
The paper investigates how Du Bois singularities behave under base change and under fiber products in characteristic zero. It establishes a descent criterion for base change using recent results to show that the Du Bois property can be detected after field extensions. It proves a product stability result: if one factor has rational singularities and the other has Du Bois singularities, their product has Du Bois singularities, and it discusses the special case of curves. These results extend the stability framework for Du Bois singularities and illuminate base-change behavior and product operations within singularity theory.
Abstract
We study the behavior of Du~Bois singularities under base change and fiber products. For embeddable varieties in characteristic zero, we show that Du~Bois singularities descend from any field extension. We also prove that the product of a variety with rational singularities and a variety with Du~Bois singularities again has Du~Bois singularities, and we discuss the case of products of curves.