On $k$-Du Bois and $k$-rational singularities
Abstract
We introduce new notions of -Du Bois and -rational singularities, extending the previous definitions in the case of local complete intersections (lci), to include natural examples outside of this setting. We study the stability of these notions under general hyperplane sections and show that varieties with -rational singularities are -Du Bois, extending previous results in [MP22b] and [FL22b] in the lci and the isolated singularities cases. In the process, we identify the aspects of the theory that depend only on the vanishing of higher cohomologies of Du Bois complexes (or related objects), and not on the behaviour of the K\"ahler differentials.
Keywords
Cite
@article{arxiv.2306.03977,
title = {On $k$-Du Bois and $k$-rational singularities},
author = {Wanchun Shen and Sridhar Venkatesh and Anh Duc Vo},
journal= {arXiv preprint arXiv:2306.03977},
year = {2023}
}
Comments
improved presentation of proof of Thm B, extended Prop 4.2 and Cor 4.3 to pre-k-rational singularities