S' be the standard conic bundle obtained from m V --~ S by one of the elementary perestroikas which are described in . 4. Let E = o"t(s), then KS. = 6" Ks+E, and , f~C C =~ d C - E if s~S\C if s~C " Hence C'+mK s, J" m E ~(C+mKs)+ l (m-DE ifseS\C ifseC " Since ~*(C'+mKs,) = C+mK s and the direct image o f an effective divisor is effective, it follows from above that the divisors C'+mKs,and C+mK S are both effective or both not effective if m > 1.
Algebraic Geometry: Proceedings of the US-USSR Symposium held in Chicago, June 20–July 14, 1989 by Spencer Bloch, Igor V. Dolgachev, William Fulton