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On a generic complete intersection surface X^2 in P^4(C) having polynomialequations z^d = R(x,y) and t^e = S(x,y) with 752 <= d <= e <= d^2/648, thereexist extrinsic meromorphic jet differentials of the form J(x,y,x',y') / [y^dz^{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 coefficientsof the polynomials A_{j,k,p,q}(x,y) satisfying a certain system of linearequations depending explicitly on R, S, the restriction to X^2 of whichprovides nonzero intrinsic global holomorphic sections of the bundle ofsymmetric m-differentials Sym^m T_X^*.

Siu-Yeung jet differentials on complete intersection surfaces X^2 in P^4(C)