Triple solids of sectional genus three

Let X be a complex projective smooth threefold and let L be an ample line bundle on X, spanned by its global sections. Pairs (X,L) as above with c_1(L)^3=3, g(L)=3 and h^0(L)=4 are classified by combining the investigation of their adjunction theoretic sctructure with the classification of surfaces polarized by an ample and spanned line bundle of genus three.