Irregularities of special C-pairs

TL;DR

This paper investigates irregularity invariants of special C-pairs, demonstrating that under mild singularity conditions, the augmented irregularity is bounded by the dimension, extending and strengthening previous results.

Contribution

It generalizes Campana's results on irregularity bounds for special C-pairs, incorporating new extension theorems and foliation analysis.

Findings

Augmented irregularity of C-pairs is bounded by their dimension

Extension results for adapted forms are established

Analysis of foliations on Albanese varieties is conducted

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.