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A tre Ac. Sci. non r6solues de g ~ o m ~ t r i e alg~brique, : Fano threefolds I, : Fano threefolds II, : Birational Math. USSR I z v e s t i a 11 485-527. Math. USSR I z v e s t i a 12 469-506. ISKOVSKIKH algebraic varieties, ISKOVSKIKH e t counterexamples (1971), Grassmanniana Rend. (19S3). ISKOVSKIKH (1978), variet~ canoniche, Questions Paris ISKOVSKIKH (1977), sulle a curve-sezioni L. GODEAUX V. variet~ 635-720. Hermann, [I1] della dimensioni, 329-356. Nuove ricerche dimensioni (1947), spaziali a cinque J.

Press to 177-202. fundamental Soc. University Contributions automorphisms 17 ( 1 9 8 1 ) , K. TIMMERSCHEIDT J. Oxford I. threefolds, On t h e J. rational [Ty] : Curven, (1974). Birational V. algebrica, rationale Berlin-Heidelberg-New IS] [Sg] varieties, New Y o r k Springer-Verlag, ~ber 163-165. Annalen of 258 threefold, in geometria 149-186. threedimensional (1982), Proc. 267-275. Cambridge Phil. CONIC BUNDLES ON N O N - R A T I O N A L SURFACES by M. B e l t r a m e t t i and P. F r a n c i a (*) Contents Introduction §i.

Is on Let C i* i*E = E Moreover linear such be E = div(s) Then we have divisor ("5" m e a n s A dimension. T i* D E T*D that V = HO(c,~(D+9*A)) the e n d o m o r p h i s m where , equivalence). d. 2) ÷ 0 = x PX ii) A2(X) iii) p ( k e r 2 ~ x) iv) the m o r p h i s m Proof. i) = Im# + p(Px ) ; ~ Im~ We have n p(Px ) ; ~+p:A2(S)@AI(s)@Px to s h o w that there ÷ A2(X) exists is an i s o g e n y . 3. p*~* = f r. ]" m e a n s the (see hence [f r . j*e*(f find e') in G(X) . p*2e) AS , relations ker some diagram , A 2 (X) ]ij (~) - T * commutes.

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