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arXiv · 2601.07318

Irregularities of special C-pairs

Stefan Kebekus·Erwan Rousseau·Frédéric Touzet
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Abstract

This paper studies irregularity-type invariants of special C-pairs, or "geometric orbifolds" in the sense of Campana. Under mild assumptions on the singularities, we show that the augmented irregularity of a C-pair (X,D) is bounded by its dimension. This generalizes earlier results of Campana, and strengthens known results even in the classic case where X is a projective manifold and D = 0. The proof builds on new extension results for adapted forms, analysis of foliations on Albanese varieties, and constructions of Bogomolov sheaves using strict wedge subspaces of adapted forms.

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Stefan Kebekus, Erwan Rousseau, Frédéric Touzet. 2026-01-12. Irregularities of special C-pairs. https://arxiv.org/abs/2601.07318

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