Singular-intersection finiteness for general semiabelian varieties

Prove that the finiteness theorem for points of tangential intersection between an irreducible curve and proper algebraic subgroups extends from split semiabelian varieties to arbitrary semiabelian varieties defined over the relevant ground field.

Background

The main theorem establishes finiteness of tangential intersections for curves in split semiabelian varieties that are not contained in any proper algebraic subgroup. The authors explain that arbitrary semiabelian varieties have a more complicated subgroup structure, so some arguments used in the paper do not directly apply.

They suggest that combining the methods developed in the paper with results of Barroero, Kühne, and Schmidt may yield the generalization, but the statement remains unresolved in the paper.

References

First of all, one may ask whether Theorem \ref{thm:split_semiab} holds for more general semiabelian varieties.

— Singular intersections in split semiabelian varieties  (2609.35307 - Ballini et al., 28 Sep 2026) in Section 1, immediately following Theorem 1.1

The formulation as unlikely intersections suggests that a generalization of Theorem \ref{thm:split_semiab_reformulated} for higher dimensional subvarieties may hold, analogue to the Zilber-Pink conjecture in Pink's formulation (see ).

— Singular intersections in split semiabelian varieties  (2609.35307 - Ballini et al., 28 Sep 2026) in Conjecture 1.2, following Theorem 1.1 in Section 1