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Theorem4AssumeCPsi1niitobeacurvecontainedinsmoothalgebraicsurfaceLetdd1ds2NsbesuchthatforeachinvertiblesheafF0ofmultidegreedwehavedegF0jBpaB18subcurveBCThenforFgeneralinPicdCjFj

Theorem4.AssumeC=Psi=1niitobeacurvecontainedinsmoothalgebraicsurface.Letd=(d1;:::;ds)2NsbesuchthatforeachinvertiblesheafF0ofmultidegreedwehavedegF0jBpa(B)+18subcurveBCThenfor[F]generalinPicd(C) jFj

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