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By utilizing Jacobian sections introduced by Stoll, we prove a second main theorem of holomorphic curves into projective spaces for hypersurfaces under certain conditions on the jets of the curves. The precise conditions are listed in three equations in the introduction. This solves a weaker form of Griffiths' conjecture and only for a special class of holomorphic curves.doi:10.1090/s0002-9947-2011-05394-8 fatcat:b5ixxuzuy5bezck6jkqishtfta