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Title: Geometry of the Abel-Jacobi map and stable birational invariants
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The Chow group of codimension 2 cycles homologous to 0 on a rationally connected manifold is known to be isomorphic to the corresponding intermediate Jacobian, as it is for divisors of any smooth projective variety. However, the geometry of the Abel-Jacobi map may differ from that of divisors, and contain some obstruction to stable rationality, for example, there may not exist a universal codimension 2
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