By C. Ciliberto, F. Ghione, F. Orecchia

ISBN-10: 3540123202

ISBN-13: 9783540123200

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Three as U T and ~ ( f , t ) %* e e C2( T), 8 E C 1 (T). % f,f ~ = O and f,s, = id. we o b t a i n %f,y = %f , ( A~* 8 - s , ( T ) ) h e n c e ~*~ £ A 2(UT). = 8"[,s,(T) Therefore = ~. s*~*~ It f o l l o w s 8 e A 1 (T), = ~ E A 2(T) . Then one has A 2 ( U T ) -~ ~*A 2(T)(D~*A I(T) "s,AO(T) = ~*A 2(T)~)s,A I(T) . d. 2. Proof. We have written in the (a,b) to s h o w form all elements f*a + f * b - i , T , of A2(U) can be for some since £ A 2 (T) • A 1 (T) by L e m m a (~,8) f,f*~ = O and Moreover f,w = n'f, 8 = n*8' with B' = f,Y ~*A2(U) Recalling 2) that ~U is s u r j e c t i v e .

On p e r i o d 75-95. : A. BEAUVILLE Inventiones [B3] which 25 ( 1 9 7 2 ) , A. BEAUVILLE Ann. S. [B2] : curves, 189-238. EAr-M] M. ARTIN e t tional A. MAYER algebraic F. ENRIQUES : Sopra una involuzione non r a z i o n a l e d e l l o s p a z i o , Rend. Acc. Lincei, s . 5 a, 51 (1912), 81-83. of 33 IF1] G. FANO aventi : Sopra tutti alcune i generi variet~ nulli~ algebriche Atti Acc. a tre Torino dimensioni 43 ( 1 9 0 8 ) , 973-977. IF2] G. FANO aventi : Osservazioni tutti sopra i generi nulli, alcune Atti varieta Acc.

2. conic fibres. that Xs f -I e(s) (s), As to exists = f*2a + f * 2 b - i , T x = f * 2 a = O. Hence, as b e f o r e = 2 a . f , i , T x = 2 a - ~ , T x = 4a, proved in [R] the g r o u p the discriminant surface a canonical is t h e s i n g u l a r for the b l o w i n g - u p divisor Then a = O we f i n d = f * 2 a - i , T x. X a n d the r u l e d There such E ker~ A2(S)4 AI(s) 2 to A I b ( S ) 4 • P i c ° ( S ) 2 , so it is f i n i t e . We return bundle f,f (a,b) contained so that O = i*f*2a is i s o m o r p h i c Since + f * b ' i , T x) is a ~ A 2 (S) 4.

### Algebraic Geometry--Open Problems by C. Ciliberto, F. Ghione, F. Orecchia

by William

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