On the classification of smooth Fano weighted complete intersections

We provide a complete classification of smooth Fano n-folds, $$6\le n\le 10$$ , such that their images under their (sub)-anticanonical embedding can be described as a wellformed weighted complete intersection of some weighted projective space and they are not intersections with a linear cone. In total, we obtain 1180 families of such Fano manifolds by utilizing a combination of algorithmic and theoretical methods.