Algebraic Geometry Bucharest 1982: Proceedings of the by Lucian BĂdescu (auth.), Lucian Bădescu, Dorin Popescu (eds.)

By Lucian BĂdescu (auth.), Lucian Bădescu, Dorin Popescu (eds.)

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Extra info for Algebraic Geometry Bucharest 1982: Proceedings of the International Conference held in Bucharest, Romania, August 2–7, 1982

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It structure with injective map M(d,r)--p(R*) its image in the p r o j e c t i v e is not d i f f i c u l t subset of p(R*) (see[l] of an a l g e b r a i c 4. THE LOCAL E X I S T E N C E In this a natural Lemma prove to see that M(d,r) 3) and so M(d,r) car- variety. OF THE T A U T O L O G I C A L section we shall from p r e v i o u s the part BUNDLE (2) of the t h e o r e m 1. R=Ri. Let p:X×Z--Z be the canonical p r o j e c t i o n and let denote Tl=U*(Ox(-dCo-rfo))O(~×iz)*(Ll) and T2=u*(0x(dCo+rfo))~(K×iz)*([2 ).

12) LEMMA. ve p l u r i c a n o n i c a l Let ups. in the DelcKI,cal. We r(X). Put Suppose sider D does the a surface since in this is true for any X with r(X)=N. Take aZI,E support. are done exceptional case surface DelcKxi curves is an e x c e p t i o n a l By a d j u n c t i o n of D', a~c. Let formula we curve by i n d u c t i o n Y with such that and D' get r (Y)-

Theorem ~. Le t n, q l " ' ' ' q i be natural numbers such that n>/2 and qj-! ~i. If n - 2 assume moreover that char(k) = o. l~,%l, .... qi ) is rigid. n+l times 1 1 Theorem io (Char(k)= o). i) Let Y be P ~ P . Then the cone C(Y,O(a,b)) i_~s rigid for ever~ a>~2 and b ~ 2 ~ ii) Let Y be F 1 and p:Y cone C(Y,Oy(b)@p~O(a)) unless a - h = 2. ~pl the canonical pro~ectio n of Y. Then the is ri6id for ever~ a > b ~ / 2 . For the proof use Theorems 3 and 4, Proposition 4, the rigidity of p l ~ p1 and F 1 and the same method as in the proof of Theorem 8.

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