2011/09/13 by Mirel Caibăr, Caibar, Mirel, C. Herbert Clemens +1
Physics and Astronomy · #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1109.2932
For an algebraic (n-1)-cycle Z on a complex projective (2n-1)-manifold X, P. Griffiths conjectured that, if Z is algebraically equivalent to zero and if the incidence divisor of Z on every family of (n-1)-cycles is principal, then the Abel-Jacobi image of Z in the intermediate Jacobian J(X) of X is a point of finite order. Using a recent generalization of the classical height pairing, we give a proof of a stronger statement, namely that the Abel-Jacobi image of Z is zero.