Unformatted text preview: (log D)) associated to (18.104.22.168) is given by cup-product with the Kodaira-Spencer mapping (1.1.3), viewed as an element p ~ Hom~ (Der (S/T)), R' f, (Dero (X/S)) (22.214.171.124) t H ~ (S, Y2~S/T) | R~ f, (Dero (X/S)). 1.4. Application to the Gauss-Manin Connection (1.4.0) The construction of the Gauss-Manin 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) (126.96.36.199) 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 (188.8.131.52) gr~(f2]/T(lOgD))'~f * ~2~/T | 12jc~i (log D)....
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- Fall '11
- Homological algebra, exact sequence, Koszul, 184.108.40.206, 220.127.116.11, 18.104.22.168