We prove a categorical homological mirror symmetry result for a blow-up of an abelian surface times C, on the complex side. Specifically, the first author's paper arXiv: 1908. 04227 provides evidence for homological mirror symmetry for genus 2 curves Σ₂ on the complex side, where Σ₂ is a hypersurface in an abelian surface V T⁴. To obtain a mirror to Σ₂, the generalized SYZ approach arXiv: hep-th/0002222, arXiv: 1205. 0053 was used. That is, (Bl⏢䃒 \₀\ V Cᵧ, y) =: (X, y) admits a Lagrangian torus fibration which has an SYZ mirror Landau-Ginzburg model (Y, v₀), known as the generalized SYZ mirror of Σ₂. The mirror to X - without the superpotential - is obtained by removing a generic fiber from (Y, v₀). In this paper, we prove a categorical homological mirror symmetry result for X. To do so, we equip the symplectic mirror with a Fukaya category which involves both partial and full wrapping in the base of a symplectic Landau-Ginzburg model. Semi-orthogonality appears in the categorical invariants on both sides of HMS.
Cannizzo et al. (Fri,) studied this question.