Title: Topological Abel-Jacobi map and Mixed Hodge Structures
Speaker: Yilong Zhang (Ohio State)
Speaker's URL: https://people.math.osu.edu/zhang.6100/index.htm
Abstract: The Abel-Jacobi map on a smooth projective curve is a group homomorphism which sends divisors of degree zero to the Jacobian of the curve. In fact, the Abel-Jacobi image can be also extracted from the mixed Hodge structure on the first cohomology of the complement of the support of thedivisor. Similar argument holds in higher dimensions for Griffiths' Abel-Jacobi map. In 2015, Xiaolei Zhao defined a notion called Topological Abel-Jacobi map, which is a generalization of Griffiths' Abel-Jacobi map to topological cycles. We will show it coincides with an alternative definition using R-splitting properties of certain mixed Hodge structures suggested by Christian Schnell.
URL associated with Seminar: https://research.math.osu.edu/agseminar/