Algebraic Geometry: Proceedings of the U. S.-U. S. S. R. by Spencer J. Bloch, I. Dolgachev, W. Fulton

H°(S,@s(D-Fi)) -~ H°(S,E(-Fi)) --~ H°(S,@s(A-D-Fi) --~ H~(S,(Ss(D-Fi)). A < 0, the first space is zero. Since (D-Fi) 2 = - 4 , by R i e m a n n - R o c h , the last space is o n e dimensional. This implies that H°(S,E(-Fi)) :# O, hence E contains (gs(Fi) as a subsheaf, and therefore is represented as an extension 0--* (Ss(Fi) --o E --~ (gS(A-Fi) --o 0.

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