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Unformatted text preview: strictness, we find (4.2.2.3.1) (1j(W,)c W,_~ c~image (I7)=(1j(W,_0. Since IV, = 0 for n,~ 0, and IV, = all for n >> 0, this implies 1  ? = 0, and hence Hz is a constant local system. Q.E.D. (4.2.2.4) Remark. Let us agree to call polarizable a family of mixed Hodge structures whose assosciated graded families gr w are all polarizable. Because gr w is exact, finite direct sums, subobjects and quotient objects of polarizable families of mixed Hodge structures are polarizable. Clearly, any object isogenous to a polarizable one is polarizable. 4.3. Geometric Interpretation (4.3.0) Let T=Spec(C), S a connected smooth Cscheme, f: X~S a projective and smooth Sscheme, and D = U D~ a union of divisors in X which are smooth over S and which cross normally relative to S (4.3.0.0) DC i X~ j ~ U=XD S 1 T...
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.
 Fall '11
 NormanKatz

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