Systematic fundamental-group computations for bred genus-3 pencils

Develop a systematic method for carrying out the fundamental-group computations associated with genus-3 Lefschetz pencils obtained by breeding genus-2 relations of type $(4,3)$.

Background

The paper constructs genus-3 symplectic Calabi–Yau pencils by breeding genus-2 relations of type (4,3)(4,3) and computes the fundamental groups explicitly in selected examples. The author observes that these computations do not yet have a systematic procedure comparable to the calculations used earlier for pencils bred from relations of type (6,2)(6,2).

A systematic computational framework would make it possible to analyze broader families of type-(4,3)(4,3) constructions and determine their fundamental groups and resulting homeomorphism types more efficiently.

References

It is also possible to obtain genus-3 SCY pencils by breeding relations of type $(4,3)$. We compute some examples in this section, although it is not clear how to systematically carry out the fundamental group computations like we did in the previous section.

— Genus-3 Lefschetz pencils on torus bundles  (2610.06440 - Huang, 5 Oct 2026) in Section 6, opening paragraph