Explicit indecomposable (2,1)- and (4,1)-cycles are constructed on Fano varieties of lines on cyclic cubic fourfolds, the first such examples on holomorphic symplectic manifolds.
D.; M ¨uller-Stach, S.The Abel-Jacobi map for higher Chow groups.Compositio Math.142(2006), no.2, 374–396
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Higher Chow cycles, cyclic cubic fourfolds and Lagrangian subvarieties
Explicit indecomposable (2,1)- and (4,1)-cycles are constructed on Fano varieties of lines on cyclic cubic fourfolds, the first such examples on holomorphic symplectic manifolds.