Entire curves in C-pairs with large irregularity

Abstract: This paper extends the fundamental theorem of Bloch-Ochiai to the context of C-pairs: If (X, D) is a C-pair with large irregularity, then no entire C-curve in X is ever dense. In its most general form, the paper's main theorem applies to normal K\"ahler pairs with arbitrary singularities. However, it also strengthens known results for compact K\"ahler manifolds without boundary, as it applies to some settings that the classic Bloch-Ochiai theorem does not address. The proof builds on the work of Kawamata, Ueno, and Noguchi, recasting parabolic Nevanlinna theory as a "Nevanlinna theory for C-pairs". We hope the approach might be of independent interest.