On a generic complete intersection surface X^2 in P^4(C) having polynomial equations z^d = R(x,y) and t^e = S(x,y) with 752 <= d <= e <= d^2/648, there exist extrinsic meromorphic jet differentials of the form J(x,y,x',y') / [y^d z^{ m(d-1)} t^{ m(e-1)}] where J(x,y,x',y') = sum_{ j+k+p+q=m} A_{ j,k,p,q}(x,y) (x')^j (y')^k (R')^p (S')^q (R)^{ m-p} (S)^{ m-q} with the complex coefficients of the polynomials A_{ j,k,p,q}(x,y) satisfying a certain system of linear equations depending explicitly on R, S, the restriction to X^2 of which provides nonzero intrinsic global holomorphic sections of the bundle of symmetric m-differentials Sym^m T_X^*.
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