An Example of Algebraic Cycles with Nontrivial Abel–Jacobi Images

In this paper, we will study a family of quintic hypersurfaces and its Abel–Jacobi images. We will construct codimension 2 algebraic cycles on the blowing-up of certain dimension 3 quintic hypersurfaces defined over number fields, and show that they are homologically trivial but have nontrivial images under the 3-adic Abel–Jacobi map.