By E. Ballico, Ph. Ellia (auth.), Ciro Ciliberto, Franco Ghione, Ferruccio Orecchia (eds.)
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Additional resources for Algebraic Geometry — Open Problems: Proceedings of the Conference Held in Ravello, May 31 – June 5, 1982
In ~(£) double [B] bundle. X is d e f i n e d exists are a nonsingular a conic canonical 6 = f,~l ima@e (3) the the proof isomorphic the point fibre of C then distinct double f-l(s) is n o n s i n ~ u l a r ; the fibre f -i (s) lines; point to a d o u b l e of C then line. 6 discriminant is o r d i n a r y The curve C of s t a t e m e n t c u r v e of X. M o r e o v e r we say that a conic b u n d l e if the d i s c r i m i n a n t nonsingular. be the the curve GI(£) f -i in GI(£) whose (s), s ~ C.
288). = 2 f is a sheaf On the and 43 other hand there exists a closed embedding % UT + ~(f,i), % which is just an i s o m o r p h i s m of d i m e n s i o n projection lines. 4). equivalent H e n c e we have = ~*Cq(T) T h e n the to a f i b r a t i o n an i s o m o r p h i s m ~ ~ * c q - I ( T ) "s,AO(T), intersection of cycles. (see q = 1,2, In p a r t i c u l a r we for e v e r y y ~ A 2 (UT): y = %, f e + %, f ~-s,(T), Since III, are b o t h IV) cq(u T) where % (see lEGAl, f is b i r a t i o n a l l y in p r o j e c t i v e [C], exp.
De F a n o de t y p e A3, B8 e_~t B14 s o n t irra- 26 Pour exemples les types h3 et 1 et 2 (3e triche discriminante th6or~me est s'6tend B8 , de d e g r 6 ~ ce 5 ; une cas). birationnellement 7. IRRATIONALITE GENERIQUE. La m 6 t h o d e Th6or~me [BI] : B~, De m a n i ~ r e de c h a q u e que type vari6t6 biennes existe suivant il : montrer Soient clair et des la courbe montre vari6t6 de ~ 4 que le de t y p e B14 IF3]. permet de r 6 g l e r : 8tre que de t y p e par en f a i r hl, h2, B2, B4, que la distincte irr6- de T, telle irrationnelles.
Algebraic Geometry — Open Problems: Proceedings of the Conference Held in Ravello, May 31 – June 5, 1982 by E. Ballico, Ph. Ellia (auth.), Ciro Ciliberto, Franco Ghione, Ferruccio Orecchia (eds.)