Frobenius integrability of certain $p$-forms on singular spaces

TL;DR

This paper extends Demailly's integrability result for holomorphic p-forms with anti-pseudoeffective line bundle values from smooth compact Kähler manifolds to those with klt singularities, broadening the scope of integrability conditions.

Contribution

It generalizes the integrability theorem for holomorphic p-forms to singular Kähler spaces with klt singularities, a significant extension of previous smooth case results.

Findings

Integrability holds on singular Kähler spaces with klt singularities.

Generalization of Demailly's theorem to broader class of spaces.

Supports the study of holomorphic forms on singular complex spaces.

Abstract

Demailly proved that on a smooth compact K\"ahler manifold the distribution defined by a holomorphic $p$-form with values in an anti-pseudoeffective line bundle is always integrable. We generalise his result to compact K\"ahler spaces with klt singularities.