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

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

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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. non razionali Torino 50 (1915), 1067-1072. IF3] : Sulle sezioni rette dello spazio G. FANO delle Lincei IF4] 11 G. FANO (1930), : [G] [I2] V. [I3] V.

F r a n c i a (*) Contents Introduction §i. Notations, definitions, and p r e l i m i n a r y §2. The C h o w group A2(X) §3. The a l g e b r a i c representative §4. The c l a s s i c a l intermediate §5. Some o p e n q u e s t i o n s . results. of a conic bundle. of A2(X) . 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) .

FANO (1930), : [G] [I2] V. [I3] V. EI-M] V. : Acc. algebriche Comm. P o n t . 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.

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