This preview shows page 1. Sign up to view the full content.
Unformatted text preview: strictness, we find (220.127.116.11.1) (1-j(W,)c W,_~ c~image (I-7)=(1-j(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. (18.104.22.168) 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, sub-objects 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 C-scheme, f: X~S a projective and smooth S-scheme, and D = U D~ a union of divisors in X which are smooth over S and which cross normally relative to S (22.214.171.124) DC i X~ j ~ U=X-D S 1 T...
View Full Document
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