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PDF-2O.DEBARREisdominant,ofdegree2:ifx02X,theintersectionofXwiththeplaneh` PDF document

HHHHHHHHHHHHHP3XJfP3JC1JCrJXisalsoaproductofJacobiansofsmoothcurveshence codimJXSing4 Thisworksonlyindimension3Theorem31AsmoothcubicthreefoldX3P4isnotrationalWew

$$HHHHHHHHHHHHHP3//______XJ(fP3)'J(C1)J(Cr);J(X)isalsoaproductofJacobiansofsmoothcurves hence codimJ(X)Sing()4 Thisworksonlyindimension3!Theorem3.1.AsmoothcubicthreefoldX3P4isnotrational.Wew

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