Du Bois complexes of cones over singular varieties, local cohomological dimension, and K-groups

TL;DR

This paper computes Du Bois complexes for cones over singular varieties and uses these results to analyze local cohomological dimensions and K-groups, advancing understanding of singular algebraic structures.

Contribution

It introduces a method to compute Du Bois complexes for cones over singular varieties and relates these to local cohomology and K-theory.

Findings

Explicit formulas for Du Bois complexes of cones over singular varieties

Descriptions of local cohomological dimensions for these cones

Insights into the non-positive K-groups of such cones

Abstract

We compute the Du Bois complexes of abstract cones over singular varieties, and use this to describe the local cohomological dimension and the non-positive K-groups of such cones.