The Hodge filtration on complements of complex coordinate subspace arrangements and integral representations of holomorphic functions

TL;DR

This paper computes the Hodge filtration on the cohomology of complements of complex coordinate subspace arrangements and uses this to develop integral representations of holomorphic functions with singularities on these arrangements.

Contribution

It introduces a method to explicitly compute the Hodge filtration for these complements and constructs integral representations with controlled singularities.

Findings

Hodge filtration computed explicitly for these arrangements

Integral representations with singularities on coordinate subspace arrangements constructed

Provides new tools for analyzing holomorphic functions with specific singularities

Abstract

We compute the Hodge filtration on cohomology groups of complements of complex coordinate subspace arrangements. By means of this result we construct integral representations of holomorphic functions such that kernels of these representations have singularities on complex coordinate subspace arrangements.