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Unformatted text preview: .., r), ds, (#=l, . .., r) Xv while f21/s(log D) is free on (_9 v with basis dxv (220.127.116.11) (v= 1, . .., c0, dxj (j=~+ 1, . .., n). Xv (18.104.22.168) Clearly the formation of f2]/s (log D) commutes with arbitrary change of base S' -~ S. (22.214.171.124) Remark. (When S is of characteristic zero, the complex I2]/s(log D) is quasi-isomorphic to j. t2~:/s. This is not the case in general, because j. f2g./s has "too much" cohomology, while I2]/s(log D) has only "geometrically meaningful" cohomology, whence our "preference" for t2]/s (log O).) 1.1. The Kodaira-Spencer Class From the definitions, it follows that we have an exact sequence of locally free sheaves on X (1.1.1) 0 -~f* (f2~/r) --~ t2~/r (log D) -~ f2~c/s (log D) -~ 0...
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- Fall '11