# Topological Abel-Jacobi map and mixed Hodge structures

@inproceedings{Zhang2021TopologicalAM, title={Topological Abel-Jacobi map and mixed Hodge structures}, author={Yilong Zhang}, year={2021} }

For a smooth projective variety X of dimension 2n ́1, Zhao defined topological Abel-Jacobi map, which sends vanishing cycles on a smooth hyperplane section Y of X to the middle dimensional primitive intermediate Jacobian of X . When the vanishing cycles are algebraic, it agrees with Griffiths’ Abel-Jacobi map. On the other hand, Schnell defined a topological Abel-Jacobi map using the R-splitting property of the mixed Hodge structure on HpXzY q. We show that the two definitions coincide, which… Expand

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