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

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

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Jacobian of a c o n i c b u n d l e . References. INTRODUCTION In this paper we s t a t e some bundles study X on n o n s i n g u l a r describe, with negative the C o n f e r e n c e A reason for this of We m a i n l y of cycles equivalent of to zero J(X) . v e r s i o n of a talk on June conic in the c l a s s i f i c a t i o n dimension. "Open P r o b l e m s (Italy), concerning the g r o u p A2(X) Jacobian is an e x p a n d e d Ravello S. 2 w h i c h are a l g e b r a i c a l l y and the i n t e r m e d i a t e This occur Kodaira up to i s o g e n i e s , codimension (*) surfaces is that conic b u n d l e s threefolds results 2, presented in A l g e b r a i c 1982.

Dbom6trique de J ( X ) . question telle singulier en g$n6ral, d~crire propriSt$ pas tr~s a un diviseur de c o d i m e n s i o n 2. on c h e r c h e r a I1 faut On e s t ne serait-ce maintenant description n'est [A-M]. lieu Nous a l l o n s une cette un description ~ cette que une Pour donc pour loin que cela dis- de s a v o i r pour classe prou- a montrer les vari6- de v a r i 6 t 6 s pour existe. t 6. FI BRES EN CONIQUES. D~finition : existe une fibres sont I1 tion On d i t surface des est coni~ues facile rationnelle sur (ou, let de c o u r b e s un qui fibr~ Sous qu'il - - si en les - sip est pest On d i t cependant le Proposition surface est Soit rationnelle la tout r~sultat la une s'il dont une les une une applica- courbe rationnelle birationnellement radu ~quivalente classe de vari~t~s rationnelles.

Alg~briques complexes, Ast~risque (1978). Annalen : Sulla razionalita delle involuzioni plane, 44 ( 1 8 9 4 ) . H. CLEMENS e t P. GRIFFITHS : The intermediate Jacobian the cubic t h r e e f o l d , Ann. of Math. 95 (1972), 281-356. [E] 21 309-391. Prym varieties Math. CASTELNUOVO Math. : are Vari~t~s 10 ( 1 9 7 7 ) , A. F. G. 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.

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