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Jun 8, 2014 at 12:52 history edited Daniel Loughran CC BY-SA 3.0
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Jun 6, 2014 at 9:05 comment added naf It seems unlikely that any of the known counterexamples to the integral Hodge conjecture would give a negative answer to your question. On the other hand, there seems to be no reason to expect a positive answer since the dimension of the space of Hodge classes could jump over infinitely many subvarieties of $B$. Interesting!
Jun 6, 2014 at 7:17 history edited Daniel Loughran CC BY-SA 3.0
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Jun 4, 2014 at 8:36 history asked Daniel Loughran CC BY-SA 3.0