Mixed Hodge structure on complements of complex coordinate subspace arrangements

TL;DR

This paper computes the mixed Hodge structure on the cohomology of complements of complex coordinate subspace arrangements, revealing a special bigrading structure originally introduced in toric topology.

Contribution

It provides an explicit computation of the mixed Hodge structure for these complements, connecting it to a previously introduced bigrading in toric topology.

Findings

Mixed Hodge structure characterized by a special bigrading

Explicit description of cohomology ring structure

Links between algebraic and topological properties of arrangements

Abstract

We compute the mixed Hodge structure on the cohomology ring of complements of complex coordinate subspace arrangements. The mixed Hodge structure can be described in terms of the special bigrading on the cohomology ring of complements of complex coordinate subspace arrangements. Originally this bigrading was introduced in the setting of toric topology by V.M. Buchstaber and T.E. Panov.