Hodge numbers of desingularized fiber products of elliptic surfaces

Each element of ( Z ≥ 0 ) 2 ( Z≥ 0)^2 is realized as the Hodge vector ( h 3 , 0 ( Z ) , h 2 , 1 ( Z ) ) (h3,0(Z),h2,1(Z)) of some compact, connected, three dimensional, complex, submanifold, Z ⊂ P C N Z⊂ P^NC . Each ( x , y ) ∈ ( Z ≥ 1 ) 2 (x,y)∈ ( Z≥ 1)^2 with y ≤ 11 x + 8 y≤ 11x+8 is shown to be the Hodge vector of a projective desingularized fiber product of elliptic surfaces which moves in moduli.