One-cycles on rationally connected varieties
2014 ◽
Vol 150
(3)
◽
pp. 396-408
◽
Keyword(s):
AbstractWe prove that every curve on a separably rationally connected variety is rationally equivalent to a (non-effective) integral sum of rational curves. That is, the Chow group of 1-cycles is generated by rational curves. Applying the same technique, we also show that the Chow group of 1-cycles on a separably rationally connected Fano complete intersection of index at least 2 is generated by lines. As a consequence, we give a positive answer to a question of Professor Totaro about integral Hodge classes on rationally connected 3-folds. And by a result of Professor Voisin, the general case is a consequence of the Tate conjecture for surfaces over finite fields.
2019 ◽
Vol 21
(02)
◽
pp. 1850011
◽
Keyword(s):
2003 ◽
Vol 120
(2)
◽
pp. 251-267
◽
2014 ◽
Vol 2014
(697)
◽
2002 ◽
Vol 16
(1)
◽
pp. 57-67
◽
2012 ◽
Vol 22
(06)
◽
pp. 1250049
2015 ◽
Vol 41
(1)
◽
pp. 81-89
2013 ◽
Vol 149
(6)
◽
pp. 1041-1060
◽
Keyword(s):