Unformatted text preview: (log D)) associated to (1.3.1.1) is given by cupproduct with the KodairaSpencer mapping (1.1.3), viewed as an element p ~ Hom~ (Der (S/T)), R' f, (Dero (X/S)) (1.3.2.2) t H ~ (S, Y2~S/T)  R~ f, (Dero (X/S)). 1.4. Application to the GaussManin Connection (1.4.0) The construction of the GaussManin connection on HoR (X/S (log O)) = R f, (f2x/s (log O)) is based on the fact that the Koszul filtration of f2~/r(1Og D) arising from the exact sequence (1,1.1) (1.4.0.1) 0 ,f* (f2~S/T) , fJ~/T (log D) , f2~/s(1Og D) , 0 is a filtration by subcomplexes, and that the associated graded complexes are given by (1.4.0.2) gr~(f2]/T(lOgD))'~f * ~2~/T  12jc~i (log D)....
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 Fall '11
 NormanKatz
 Homological algebra, exact sequence, Koszul, 1.3.1.1, 1.3.1.2, 1.3.1.3

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