Terminal Fano fourfolds and anticanonical linear sections

We study terminal Q[jls-end-space/]-Fano 4-folds of index 1 realized as complete intersections in weighted projective space and their anticanonical linear sections. We first construct families of terminal Q[jls-end-space/]-Fano 4-folds of index 1 in low-codimension weighted complete intersection models. We then investigate whether the anticanonical linear system contains a divisor that is a quasismooth Calabi–Yau 3-fold with isolated canonical singularities. Building on Qureshi (2025), which treated the cases h0(−KX)=0 and h0(−KX)≥2[jls-end-space/], we complete the analysis by addressing the borderline case h0(−KX)=1[jls-end-space/]. We also enlarge the list of examples in the previously studied cases by performing computations with larger search bounds.